The problem with your method is finding that "non-KYC exchange" because they are hard to come by and those that exist are risky to use because they either enforce KYC in a hidden way or they are shady!
Your approach will also cost a lot in fees and other costs such as the fact that sometimes buyers of your coins in private will buy it at a much lower price (like if you want to sell XMR to BTC).

I think buying with cash and from individuals is more private and will cost less. Then you an run the coins through a mixer. Or as it was mentioned earlier just buy bitcoin as first step instead of XMR and run that through a mixer.