mentioned pedaling - maybe something like this
I found learning to crochet easier than learning to knit, which I never really mastered. It still uses both hands, but only one hook. As far as what to make, here
are some categories of patterns. It does get annoying to amass items you'll never use; I don't really have a solution for that one.
Something else I do is go through hand-strengthening exercises with a stress ball. I don't know how mindless that would get for you, but maybe use a variation of exercise types?