When we can count coingecko and CoinMarketCap as part of research maybe not a solid one... even a reputable exchange can still be having the issue of getting accused for stolen fund although most are due to negligence, it will be so hard to come to conclusion just have you've said extensive researchis required.
Let us know what is your best way how to do research that even using reputable exchanges could get you into trouble for stolen funds issue, you can't call it reputable if that's what they are doing.
There can also be a rest of mind to choosing a non custodial wallet over an exchange wallet Although that also need research but there are reputable ones like Blue, sparrow and Electrum exchange ge could be done on sites like
https://exch.cx/ since they might not support auto inexchange (swap)like exchange wallets
Wallet is wallet, not an exchange, you can exchange of course on other non-kyc platform but that's their limit, most people uses exchange is to regular trading either it's spot, future, etc. You can't force someone to use non-custodial wallet instead and follow your way of doing exchange