What's the risk to the funds if everything is on the up and up? Why are you worried about KYC if everything is clean?
You should have no problem using Kraken, Coinbase, or any other major exchange. If your current bank is crypto hostile, just insert another account in between it and the exchange. Zen, Verifo, Gurupay, and other crypto friendly EMIs. Money goes there, then to Kraken. Easy stuff.