Oh it's hard to explain through text but definitely don't hold your thumb on/over the neck. Your fret hand should be same or similar as playing guitar. Your thumb should be usually pretty much "on the spine"/middle of the neck. If that feels uncomfortable, you might be holding the guitar awkwardly/wrong. Check out how people instruct you to hold classical/Spanish guitar, because that's literally like guitar ergonomy 101.

My problems with my fret hand were mostly related to having too wide a neck for my hands which led to over stressing my fret hand, pressing too hard and having my wrist at an awkward angle. Which led to pressing even harder which led to wrist pain and overall difficulty reaching everywhere I was supposed to. Things you should take into consideration but not necessarily stress if you're just playing to chill, but I was ambitious from the get go.

The way you describe "crab claw" sounds about right, but you can check out classical/Spanish guitar + wrist + ergonomy on YouTube or something if you want to. Your wrist should be fairly straight and you definitely can't do that if you're having your thumb over the neck. As little as your nerves and tendons and shit need to stretch unnecessarily, that's the sweet spot. Look at how classical guitarists play. They have the guitar at an angle for a reason, because they're kind of going to the extremes of the mobility of the fingers and tendons etc, and even if you aren't, a more ergonomic stance is only going to do you good

E: almost forgot. It might do you good, especially for something as small as a Ukulele, to get a strap. It can be difficult to hold and fret and do all of that at the same time. A strap can make it a lot easier/automatic for the instrument to stay in a good position so as not to strain your wrists