Selling KYC coins for non KYC

I have some shitcoins I bought on an exchange, I wanna sell them all and get some of the money back and then buy non KYC BTC. I don't want any of this to be linked to a wallet I'm using, which has not had any coins on it yet.

I haven't made any profit with what I'll be selling.

So if I understand this correctly this will not be linked to the wallet I'm using? I will not be moving any of the coins to it and I want to shut down the account I have on the exchange.