USB heated Gloves mod Qs

I recently received a pair of USB powered heated gloves. Unfortunately they have a big bulky switch that hangs too closely to your hands and dangles around when you type. I'm looking to mod the gloves to have a less clunky switch, something more streamlined. The gloves have three setting, High (II), Off (O), and Low (I). There's a pic of what the inside looks like. I'm trying to figure out how the circuit works. I would assume it was just one setting is full power and the other has the resistor in it, but the resistor appears to be soldered to two leads on the switch. Does the wiring of it mean it skips the resistor when it's in the high position? Also what type of resistor is that (the big grey type) can it be substituted for a smaller one of equal value? It's not that important, I'm just curious, because I think I'm actually going to make the mod only have the High setting and probably without the switch since I could just unplug them instead of adding in a switch.

I think the heating elements might be wired in series because the top pad doesn't get as hot at the bottom (or maybe they're just different temperature pads?).

And I'd like to add a battery pack option. What would be the ideal (smallest) batttery setup I could use? (5 volts right?) Would a 9v battery overwork the thermal pads or just make them hotter?

I was also thinking of changing the connecttion to a connector like this (LINK) a might be a little smaller, thoughts? Also what wires on the USB are pos and neg?

Picture of USB heated Gloves mod Qs