You can stake on noncustodial wallet through validators. I think you can also stake in a noncustodial way by providing liquidity. I do not really understand how the later is but I know about the former.
I read a thing or two about validators some months back but quickly forgot about it, maybe cause I wasn't interested in staking to start with so had no desire to do more research on it. Anyone with good knowledge on how it works and the security it provides that can definitely give it a try.
Providing liquidity means you give proof of funds without having to lock it or you're referring to liquid staking?