Is it required to have a promotion ceremony for a SPC?

I think technically it is an "advancement" ceremony until you make E4, then "promotion" to E5 and beyond. But aside from that, there is nothing wrong with your desire if it is out of modesty or not wanting to draw attention to yourself. But keep in mind promotions and awards are for the people around you too. There is probably a private who looks up to you/hates your guts, who will see you get promoted and say "I want to be like SPC Szafarski" or "They promoted him?!? I know I can do it then." If you want to be humble, when you get the floor after you have the sham shield affixed to your chest, thank everyone you can think of, attribute your success to your teammates (it is true to a degree no matter what you may think) it is not a burden, it is an opportunity. Trying to find a regulation that says "In accordance with establish regulations, I don't have to." might not be wise. At some point you might turn in a leave form a day after the suspense, in a normal world, your PSG will process it anyway, but what if he says: "I'm sorry, in accordance with posted policy, I don't have to."? Don't make waves, get promoted, be happy. (Oh and if you are not using tuition assistance, start now.)

Although not required it is a good opportunity to establish connections. Tradition however is that a small ceremony is good for the unit. I had a small ceremony and went home to the house for a nice dinner with my wife.

SPC (Join to see)
This is what I'm seeing per the AR 600-8-19 Enlisted promotions and reductions

"1–24. Promotion ceremonies and certificates
a. Promotion ceremonies [WILL] be held on the effective date of promotion. Early promotion ceremonies may be held when the effective date of promotion is on a nonduty day.
b. The promotion certificate is not the official instrument for promotion. The promotion order will be used as the source document for rank, effective date, and DOR for all record and pay purposes.
c. A Soldier who is reduced one or more grades will receive the appropriate certificate when again promoted.
d. Promotion certificates for Soldiers promoted to SPC and above will be prepared by the unit or BN HR activity for signature by the SGT and/or SSG promotion authority. Any higher level CDR may direct that signature authority be held at his or her level, but the certificate will still be prepared by the unit or BN HR activity."

Unless the word "will" is being used as a definitive term I don't see a problem with declining the ceremony, perhaps those with more experience here can give you a better answer.