How to use aquafaba without a hand mixer?
In theory hand whisking should work but it will take quite a lot of whisking. Personal opinion I don't think it is worth the time you will spend whisking. But I do not like the taste or texture of the whipped aquafaba. If this is something that you might want to do more often I would spend the $20.00 and get a hand mixer, or even less and get one from a resale store. Just make sure you plug it in before you buy it to make sure it works
The blender or food processor won't cut it with eggs, so I'm guessing it won't for the aquafaba either. Get a big glass or metal bowl (don't use plastic - at least with eggs - any trapped oils keep them from whipping up) so you can be sloppy and not shoot it everywhere - and start whisking. Do you have any family or roommates to help take a whisking shift ;)