This may sound a little odd, but a bike balances by steering rather than by you balancing it, so in fact a dodgy sense of balance isn't a major issue :) Hearing impairment is no problem, & I regularly teach 10-yr-olds who don't drive either & often have only minimal road-sense ('can cross road without being run over' is about it :) ). Visual weirdness: as long as you can see other traffic coming, you'll be OK (it might need some adaptation, & it's certainly something that anyone teaching you would prefer to know about, but they're your eyes & you already know about how to work with them!).

So even if it is a scary prospect, it's not a crazy one :)