As DrDrumble mentioned, foot pedals would probably be the best. But if that's not possible, there are buttons called "switches" that will do what you want. The only issue here is that you need a mouse with 3.5mm ports so that you can plug in the switches to work as replacement mouse buttons.

I also have a lot of pain and dysfunction issues with my hands and arms. My favorite switch is a little pricier, AbleNet Micro Light Switch.

There's also another switch with a little higher activation force that would also work, Ultra Light HD Switch. However, I haven't been able to find this one on amazon.

I could only find one, but perhaps other people know other mouse options. Switch Adapted Mouse

Having said all that, there might be a better and different solution than what I've presented here. Seems like the simplest for you would be the foot pedals, unless someone else can offer another solution!