Did you convert your BNB to USDT when you withdrew them?
Keeping those BNBs out of a mixer will not be worth keeping if all other exchanges are informed about this tagged BNB from your hardware wallet. If you still have those BNBs, maybe you could try selling them to some other exchange for USDT this time to see if they allow them or if it's just Binance. Exchanges will likely kill the mixers if they all have this policy.
As I can remember, I converted them to USDT and bought altcoin, and later I withdrawn altcoins. They were suspending only withdrawals but allowed me to trade. But when they enabled withdrawal, then they disabled all other functions. So I don't feel any risk right now. I moved them to another exchange and traded there. The rest of the funds moved into the hardware wallet. So I believe intentionally they won't freeze my BNB since they don't know where I store my funds right now.
