Physical effort in outputting 5V 1–2A?

20 watts delivered into a hand-cranked generator (enough to deliver 10 electrical watts after conversion losses) could be managed all day by a fit and motivated person. This would employ all of your arm muscles. However, you'd need reasonable length cranks, comfortable handles, a good secure mounting for the generator, it's not something you'd nonchalantly carry onto and use on a bus.

A grip-squeeze device could be rigged to generate some power but, only being able to use the small grip muscles in the forearm, you'd struggle to get more than a few watts for a few minutes before exhaustion.

If you don't mind standing, then a mini-stepper could be rigged with a generator. This would use your legs, so we're back in the sustained many 10s of watts, even 100+ region. It could lie stably on the floor, and maybe fit into a small backpack, so is probably the most suitable device overall. Consider that a 70kg individual walking up 200mm high steps one per second is delivering 140 watts.

Neil_UK’s mention of hand grip strength training devices made me curious how much power your hands could provide. To get an estimate I looked up such devices, apparently they usually provide about 500N of resistance over a distance of 6cm. This gives us about 30J of mechanical energy per squeeze. Not sure how many squeezes you can do per second, so let’s go with energy. A NiMH AA battery cell stores about 12kJ of electricity, so you’d need 400 squeezes to charge a single NiMH AA battery. Good luck with that! And this calculation doesn’t even account for losses.

As Neil_UK also mentions, arm and leg muscles are much stronger. Even an untrained person can output 100W on a bicycle over long durations (>1h).

10 watts compared to the 550 foot-pounds and 746 watts of ONE Horsepower, gives us useful numbers.

You need to lift 550 foot-pounds * 10/746 = 550 * 1/75 ~~ 8 pounds lifted up ONE FOOT, every second.

Can you lift a gallon of water, every second, up one foot, for an hour?