There are thin body ukuleles, which might take care of the feeling of the body of the uke being a bit too thick for you when standing. I've seen LoPrinzi and Kinnard list thin body ukuleles, and would assume that others have them as well.
This is from a listing of a Kinnard thin body tenor up for sale right now:
The Kinnard "Thin Line" models feature a body depth of 2" vs our normal body depth of 2-7/8"
I've seen thin body concerts as well.
Rebel makes slimline "Cheese Cake" and "Creme Brulee" in the three sizes. The standard depth bodies are called "Double Cheese" & "Double Brulee"