How do you tactfully and respectfully refuse an unlawful order without getting in trouble?

It is best to acknowledge the NCO who told you to change your socks and drive on. All you had to do after the fact was notify your first line leader about the misunderstanding so they can fight the battle for you. As you hopefully learned, arguing the case with someone who has direct influence over your fate does not help your situation. Sometimes you have to choose your battles wisely and spend a little gas money versus getting hemmed up over something stupid.

Most importantly, now you know what *not* to do when you're the senior leader and I hope you now understand how to navigate situations like this in the future. Thankfully they are uncommon but at least you are equipped with the knowledge. Drive on and have a great day!

You're right, she's wrong. However...
Here are 2 things I often say to people in situations like this is:
1. "I didn't ask if you were right. I asked if you HAD to be right." There's a difference.
2. "Is this a hill you're willing to die on?" If not, let it go and change your socks.

Well first off NCOs give Lawful orders and Officers give Direct orders, but heck that's just semantics. Anytime you buck up to a senior individual you stand the chance of catching heck, depending on their level of self confidence, maturity and if they are reasonable or a dipshit. Uniform regs change quicker then some folks change their skivvies lately so it's not surprising there would be an encounter over the propriety of some uniform item or another. The best way to avoid an incident is to be respectful, and not get into a public exchange.
What worked for me when someone made an incorrect -correction was to politely ask them to step away from earshot of others and explain their folly. Sometimes it worked, sometimes it didn't, when it didn't I'd "yes SGT, NO SGT" disengage after listening to whatever horse manure was shoveled and report the negative encounter to my NCO and drive on.
So again read the third sentence of the first paragraph, there is no guarantee that you won't catch some form of crap.

Should've changed your socks, since the order was not unlawful.
Then printed the appropriate section of AR 670-1 and tactfully explained the change and as of date.

Sometimes you can be wrong by being right.
This is all a big misunderstanding though, so long as you don't lose your mind.
If she tweaks about being squared away (you never know, I've seen this plenty too), go up a level.

Damn, I hope she never sees my socks. I don’t own any color but black.

Right so first off it was not an unlawful order. The NCO May have been wrong but not unlawful and in this case you were wrong. You may have been understandably frustrated, but you should probably be or get used to that if you plan on staying in the Army. Best course of action here would have been to say that the 670-1 had changed. Of the NCO restated the order then you acknowledge and do as ordered. If that NCO was not your first line supervisor then best to go to yours and have them handle it.
In no case should you or do you have the authority to disobey without consequences.

It was NOT an unlawful order to change your socks. You are an NCO, so should know the difference between an unlawful order, and an error or misunderstanding of a regulation. Further, this is why it pays to know paragraph and line number, or message number when changes are made.
I suggest that since she isn't in your COC or NCOSC, she lacked the authority to direct you to absent yourself from your place of duty, if you were at your place of duty, or about the business of your duty.
I also am of the opinion that she lacked the legal authority to direct you to change an authorized uniform item, since it wasn't in violation of regulation or policy. The commander establishes the duty uniform, which (if) you were properly in.
The likely reason you haven't been counseled by her is she likely checked and learned she erred.
However, If you were insubordinate in tone, or otherwise, that's your fault.
Best response: Assume the position of attention, than parade rest. Clarify the correction being made. State paragraph and line number, or message number, if you believe the correction an error. Wait for response. Yes, Sergeant, no, sergeant. Request permission to carry on. Immediately report what happened to your supervisor. I have seen circumstances where an on-the-spot correction escalated to disrespect to an officer (or NCO). Had one where my commander made an OTS correction for an authorized religious item, and after I told the commander and Soldier that it was authorized, I gave the Soldier a significant emotional event for the insubordinate tone, failure to go to the position of attention, and arrogance to believe an error granted him license to be disrespectful.
In circumstances where the "correction" could be made immediately, I would agree with making the "correction." For the reasons given above, there was no need, or requirement, to change your socks, not was their justification to become insubordinate.
I would argue if the insubordination was your failure to leave and change your socks, that wasn't insubordination, but I'm not your supervisor.
That NCO need to be aware of current regulations and policies if she wants to make OTS corrections, and you need to learn not to be insubordinate.

You see you were doing good until you said "I'm not changing my socks". Assuming you were to disobey an obvious unlawful order there's a process. If your NCO orders you to do something illegal then you have to do a few things. First, ask them to clarify the order, as maybe you just misheard them. Then explain your objections by citing regulation or law, then if they are insistent on you still carrying out the order then you state that you can not follow the order because it is unlawful.
Being out of regs isn't unlawful on it's own. I remember in basic the drill sergeants would make us do all kinds of unique uniforms that were not in the regulation, if you ever played the changing game. There has to be something outright illegal about the order in order to refuse to obey it, like "park in this handicapped spot", or "attend this briefing that you don't have clearance for" OR "kill these POW's".
If the order is just something that you don't agree with or that you think the NCO is mistaken about then you should follow the order and then follow-up later with your NCO or chain of command or NCO support channel and address the issue. For all you know there's a unit or post policy that superceeds the regulation.

Tactfully take the regulations to your NCOIC and show them then ask (respectfully) them to explain how you were out of regs and insubordinate to the Senior NCO.

So many things wrong here.
Your thread title: the NCO did not give you an unlawful order: she never told you to do something illegal, she wasn't even directing you to violate AR 670-1.
The NCO was wrong, in that NCOs do not give "direct" orders.
You could have handled it better when talking to her, but good on you for not using the excuse of changing socks to bail on PT.
She hasn't counseled you because after the confrontation, she opened AR 670-1 to start the counseling and realized that black socks were authorized over 3 years ago and she somehow missed every story about it. I would hate to think that this happened because she has not conducted PT or even seen others conducting PT in over 3 years.
She was still pissed about how you handled your side of it and went to your NCOIC.
There's better options to address a misinformed NCO than just flat-out saying "I'm not doing it" or "I don't have to do it".
Personally, I thought black socks with shorts looked bad in the 1970's, and I think it's a bad look today.