I have used this for years: http://www.amazon.com/Logitech-910-000806-Trackman-Marble-Mouse/dp/B001F42MKG
It's not hand-held but can rest on almost anything.
For ergo relief, what I do is arrange my desk in an L-shape and rest my elbow and forearm on the side part. Because I use the trackball, my arm doesn't have to move. I've done this for years and it's been great for preventing shoulder strain and carpal tunnel problems.
Regarding the scrolling steps, if you like you can configure the trackball to use the ball to scroll instead of the wheel. You would hold down one of the buttons (you should be able to configure it to use any button) and then move the ball to scroll, that's kind of similar to the inertia on the scroll wheel. That's what many people do with the Logitech Trackman Marble, since it doesn't have a scroll wheel or scroll ring.
There are a few ways this can be done in Linux, the Arch wiki lists some.
You'll see the ones with the ball in the middle referred to as "finger" balls a lot of the time. They're usually larger balls that can be used with either your left or right hand. To me, the mechanics of using one is a lot like using a touch pad.
With a thumb ball the mouse buttons are usually set up like a normal mouse, but with a finger ball they'll be on either side of the ball.
The 575 is great for beginners, or... for those with thumbs. Lol
A basic finger ball you can try for cheap is the Logitech Marble, but I don't know if you can get a wireless one. There is also the Kensington Orbit with a few more features including wireless connection for a bit more cash. https://www.amazon.com/dp/B001F42MKG/ref=cm_sw_r_apan_glt_fabc_KWGB7WQV9ZA7HJW8S9ZX
https://www.amazon.com/dp/B0050SPZMK/ref=cm_sw_r_apan_glt_fabc_HXQA9VQTVRZSWD3KH3YZ
I suggest trying both styles, and then returning the one that doesn't work for you.
No matter which you prefer, there are plenty of upgraded versions you can choose down the line!
I realized i failed to attach a photo to this post, it’s this “mouse”:
I find that tracker balls like this work better than a mouse.