So in theory, if you do p2p trading, and your exchange account, which has your KYC so all your information, is the place you send crypto to someone, and you get cash from that person, as in banknotes in a duffel bag type of deal, then IRS will not know, because exchange will not share that, it's only the banks that share this information because you withdraw it to your bank account.
If it is a 'Bank notes in a duffel bag' type of deal then using the Exchange account with Know Your Customer procedures verified is not the best idea. There are a handful of Know Your Customer free Centralized Exchanges at least that you could use instead. But even then, why use the Exchange as a way to spend the Cryptocurrency? Why not simply send it to their Wallet instead? You could move around with zero head aches even if you never complete the Know Your Customer procedures.