I have very large hands and fingers which is marvelous for playing bass guitar but I end up covered in blisters whenever I've attempted to solder anything. Its also a pain in the ass if/when it goes wrong and I lack the extra pair of hands necessary to hold the wire, soldering iron, solder and pot all at once. This leads me to favour brands like EMG whose quick connect system is a godsend, so long as you want modern sounding active pickups.

So are there other solderless options? I.e. pots with screw terminals, easy wire connectors, etc. Anything to stop me scarring my hands even more?
You could probably use spade connectors on the pots, but it really wouldn't hold well.

You could also use something like this;

You'd need to have one end soldered to the pots & switch etc. but then you'd be free to change pickups whenever you wanted.
All wires would have to be hard-soldered to the pots - but you could use any form of electrical caps to connect the cables. Just make sure they are small enough, and have a tight fit. Home Depot or any other home improvement store should have a nice electrical area that will have everything you need.