Can I wear my Airborne and Air-Assault badges while in basic training?

I would definitely for graduation. Not sure how much it matters one way or the other going through basic again. I presume everyone would be able to tell quickly that this isn't your first rodeo.
Should really have that talk with your recruiter about having to go through basic again and not just going straight to a Re-Class AIT (I'm surprised its a requirement if it's only been a few years).
But wear what you've earned.

There really isn't a "should" or "shouldn't" here, just regulation, command policy, and personal choice.

Army regulations authorize qualified personnel to wear both of these skill badges on the duty uniform. This is Army wide and for all Soldiers unless countermanded, by exception, through command directive. There are some units that are command-directed to wear badges differently than proscribed in the regulation and there are some schools that modify the uniform while assigned- Ranger School comes to mind. These modifications start at higher levels of command and are not decided by Drill Sergeants, as they are bound by the same regulations you are and require deliberate command override to institute. All this to say that you are authorized to wear all awards and badges earned in your previous enlistment (on the proper uniform) until a countermanding command policy is made explicit to you. If that occurs, just be professional about it and there will be no foul.

Now, when considering what you will choose to do, remember that these badges represent successful completion of two schools that required you to be bold. I say run with that trend and accept the leadership responsibilities that your Drill Sergeants will look for you to carry. You will probably be an NCO soon, so I recommend using every opportunity to learn to lead since the mistakes you make while achieving will be worth more to you than all of your mediocre successes. Besides, your Drill Sergeants will already know that you were prior service, so you won't be hiding anything. While you may choose to, or not to, wear your skill badges, I would hope that you can see that you really don't have a choice if you accept your role as a future leader. Plus, as it is often said, "fortune favors the bold", so be bold and face the heat.

You earned them. Wear them proudly.

Do not do this. Just lay low. You will be a target for your DS. Don't let anyone know you've been in already. Go ahead and wear it when everyone is wearing their Dress Uniform at the end.

I wouldnt wear anything at all.

The ultimate answer is to look at tge 670-1 wear and appearance of a military uniform all your answers regarding whether you wear it or not is right there!

Homework time write down all pros and cons and then make your decision. Could go either way for you depending on how high speed you are in basic. So you seriously have to look at yourself and determine how is your performance gonna be.

I would only wear them if they were sewn on. This will eliminate the drill sergeants eating your lunch if one of them is pinned on out of regs. Plus time management should be an issue, but I haven't been to basic in over 20 years so things have changed. Finally you need to take something that proves you have earned these badges. If the drill asks for proof and you can't produce it, then it is like you never earned them.

If you have earned them, then why not wear them? You may catch a bit of extra attention from your drill instructors, but that's nothing to fear.

My Station Commander at my recruiting Station told me more than twenty years ago that back in the 80’s he left the active duty Marine as an E4 and joined the Army Reserve and worked through the rank and became an E6 with a qualified Drills Sergeant batch. Then he decided to join Army Active duty, the Army dropped his ranks from SSG to PFC. Back in the late 80’s, the Army doesn’t need too many soldiers. In fact, the Army even paid incentive to Soldiers to get out being Active duty or Reserve. My Station Commander almost walked out of the MEPS, but due to his circumstances back then he decided to kept his pride and accepted the offer as a PFC with the new MOS that required him to attend AIT. At AIT, all his chain of command know that he was a Private with a qualified Drills Sergeant batch excepted the Post CSM. One day, at DFAC (back then we called mess halls), Post CSM saw him as a PFC with DS batch and a student at AIT. He was stopped and asked about why he worn the DS batch, but before he gave the answered his 1SG came and gave the answers to CSM. And from then on, CSM gave him a new name as Private First Class Drills Sergeant!
For you now, since you’re qualified and earned the right to wear those batches, you should wear them proudly because no one can take away from you since it’s in your military records.