Can I remove individual conductors from a 12/2 cable to act as jumper wires for a switch?
You're talking about a pigtail and it's perfectly OK to shuck down NM cable for pigtails.  (or UF cable if outside). 

I'm a little concerned your built-in wires are not long enough.  The wires should stick at least 3" out of the box, although even that is uncomfortably short.  If the box is large enough to get your hands in there, then 6" from entry to the box will suffice, but this too is fairly short.  Electricians prefer more like 8".  

Pigtails do not count toward box fill. 

If you are having trouble physically packing all the wires into the box, then you have definitely exceeded the allowed box fill.  It's time for a box extension.   A variety of box extensions are made.  For boxes sunk into finished walls, try Legrand Wiremold "starter boxes", which give a 1" or 2" lift to allow you to start running surface conduit off them.  Don't attach any surface conduit. 

If the bulky thing that won't fit is a GFCI+receptacle combo device, you only need one GFCI device per circuit, and it can be located elsewhere.  It can go anywhere upstream on the circuit (closer to the breaker panel) - such as another receptacle, a GFCI+circuit breaker combo device, or an added location near the service panel.  I do a lot of the last one.