I don't think any big exchanges would accept you using mixers to transfer money to them. Pretty much all CEXs imo would have some kind of law/precaution with regard to mixers since they hide potential money laundering transactions and in such cases, they just choose to ban everyone who tries to use them.

I'm not familiar with how CEXs track tainted wallets but wouldn't the other wallets be fine? I mean if mixer > wallet 1 > wallet 2 > wallet 3 was the process, then any wallet that has sent coins to those 3 should be safe. I can't say the same for any wallet that has received coins from those 3 though since they may tie it to the coins received from the mixer. To be 100% safe though just avoid using any of them I guess? P2p might be the best option for your current existing funds.