Here in Reno there is a one arm amputee Vietnam veteran who uses a bike as his sole transportation. All controls are on one side of the handlebar. In fact the other half of the handlebar has been cut off as he does not wear a prosthesis.

No help to you as you are dealing with a double amputee but it does show what is possible with determination.

One possibility I can think of is a bike or trike with the new Dura Ace electronic shifting. Shifting can be done via switches that can be hit by prosthetics I would think. I am not sure about how to manage brake controls however.