I mostly do not use a strap, either standing or sitting. That being said, I do have a couple of straps (leftover from my guitar days) and have no problem fitting them if I think I need one.
When do I think I need one?
Gigs. If I want to walk around and have the ability to carry something AND have my ukulele safely out of the way, like on my back, I will use a strap.
Also, While I can stand and strum and not worry about holding my ukulele (left hand barely supports the neck, the real "clamp" is with the forearm against my body. I strum at the wrist, so I don't need my elbow joint to move while playing.
I do find that more elaborate fingerstyle does necessitate that I re-position my wrist somewhat, and that makes it a bit more of a challenge to hold the ukulele while standing, but seated I am just fine.
.....+1....