I have a gaming mouse that has buttons on the right-hand side of it, that can be remapped. Maybe something like that would help? I mean if it's on the right and you can only use your left-thumb, maybe that will work out better?
I think maybe a trackball will work for you - as well - I'm sure that they have them for left handed people, usually the ball itself is how you move the cursor around. It's on one side of the mouse. That way you can move the camera around with the trackball and navigate normally. A lot of them also have different buttons that are in the same are in the same place.
This might work - it looks like it's for either hand...if you only have the left button (I'm going on what I read before), what you could do is mount it and and just use your left thumb to either roll the ball around or push the buttons. It should work the same as a regular mouse:
You could remap the keys on the top to do the go forward and interact functions and just click them when you need to.
And maybe I misunderstood what you were saying but I took it to mean that you could only use your left thumb at all - and I thought this might work at least while you are in game.