This is for one use: Hair on the bathroom floor. 60 seconds every 2 days,
when I don't want to haul out the big canister vac.

It's been a very long time since I've owned one, but for that use, I'd be
tempted to look into a wall-mounted cordless unit. Used to be called
Dustbusters back in the day. I'm usually not a fan of cordless units, they
typically don't have the suction of 110v units. But hair off a tile floor
(I presume it's tile or some hard surface) is an easy pickup. Not a lot of
suction required. I'm thinking that battery technology has improved greatly
since I owned one of those things. For your specific use, I think I'd go
with the convenience of a nearby wall-mounted cordless rechargeable unit.
No messing with cords and potential electrocution hazards, and no bothersome
belts to worry about going up in smoke.