Yes my right arm has a nerve complication that makes it tired easily so being a bit lighter can be more comfortable, thanks for the insight! So the headstock is purely for the looks?
I agree, definitely talk to your luthier about your situation and see what he/she can do to help. Here are some considerations:
Ask about the woods. I have a lightweight Ono spruce/rosewood tenor, so it’s not an absolute that Rosewood will be heavy. The type of rosewood and the build is what will determine the weight. Mango is a fairly light wood. Walnut can also be light.
You might want to consider a uke design like the Rebel Creme Brulee. It has a less deep body, but still produces excellent sound.There are several makers that produce “travel” ukuleles with shallower bodies which might be an option. Kala and Ohana come to mind. The added benefit, besides less weight, is that they are very comfortable to play. Ask the luthiers if that is something they can offer.
Another option might be a long-neck concert instead of a tenor to reduce the weight.
Rounded edges on the body, especially the top should be beneficial. This prevents the edge from digging into your arm and putting pressure on the nerves. An arm rest is is even better. Though the tradeoff is a some added weight.
If the builder uses a truss rod in the neck of his tenors, a carbon one will be lighter than a metal one. I don’t know if a walnut or maple fretboard will be significantly lighter than a rosewood or ebony one.
I highly recommend using a strap. Without a strap, your right arm has to hold the body as well as strum and pick, while your left is supporting the neck as you try to fret. A strap frees up your arms so you can concentrate on your playing and not worrying about holding the uke. It would help reduce the work your right arm has to do.
The wider the strap, the more the weight is distributed on your shoulder. I use 2” wide guitar straps on all of my tenors because it is more comfortable to me. NeoTech has guitar straps with some neoprene in it. This allows a little stretch and give which absorbs some of the forces from playing and reduces the stresses on the shoulder. I have one on my very heavy banjo uke and it does help. They also make a harness that is designed for heavy solid electric guitars and basses. It might be adaptable for a ukulele. (Amazon carries them.)
Sitting and playing may allow you to rest a larger uke on your lap as you play. A strap still helps to control the neck. And, bonus!, prevents the uke from falling to the floor when you stand up. (Don’t ask how I know.
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Like all advice, take what you think makes sense and discard the rest.