Most of them just have a slot for your room key to turn on the electricity and/or A/C, but many times it is a physical which i.e. it doesn't care what gets stuffed into the hole and often there is some kind of brochure that can be folded/ripped into card shape to trip the switch.

Ask for a second key and leave it in the slot?

Those slots don't require a specific key. Put your library card in there and it'll work fine.

They get suspicious when I pay for X occupancy but request X+Y keys.

Hotels routinely give me two cards when I check in--and certainly will if I ask. I usually stick one in my wallet and one in my bag or whatever so I'm less likely to accidentally leave the card in the room.

Usually you can stick anything that has the correct form into that slot. Even thin cardboard :)