I would say maybe not look for a no KYC exchange. I mean if you want to use an exchange, you can't get any better than Binance and they will do as best as they could every possibly do for every single customer since that would be the key to their success and they are bigger than most banks in the entire world so you know they are protected like fort Knox, there is no problem there. So giving your KYC to them shouldn't really be a problem, unless you are a criminal.
On the other hand, for all the "under the radar" moves that you want to make, you could use DeFi, like pancake or 1inch or whatever you want to use, and that way you could move it around with a custodial wallet like metamask, and everything will be sort of hidden as well, only the entry and exit will be known, rest will be hidden.
I agree with this, there is no situation where you should be considering KYC and feel fine about it. Because if you are not giving your KYC to a place, how legit could they be? I mean if a place is asking for your KYC that means they are forced to, because they are legit and they comply with the laws of the nations they are working with and KYC is part of it.
If a place doesn't ask for your KYC that means they don't really care about the laws, and they just operate in a pirate way, which means if they are "hacked" like all the many that happened so far, there is absolutely nothing you can do, and all of that money is gone. Which is why it’s too dangerous.