The .30-30 should be able to work. But, a necked cartridge needs more barrel to pick-up speed for the lighter bullets used. Personally I would lean towards a handgun caliber like the 44, 45, etc. You could have a shorter barrel(10"-8") that would move out pretty good. Heavy for caliber moving at a modest pace would sit them down. A 41 mag, or something similar, would be be manageable with a shorter barrel. I am 50yoa, and if I could only use one arm that is the way I would go.
Also, Are you limited to your less dominant arm or your dominant arm? TO ME a 12" barrel one handed would be kind of unwieldy and awkward. A shorter barrel would be much more manageable, and to me that says heavy for caliber handgun cartridge.