Another option I didn't say is simply to pinch the wire between the thumbnail and index finger and pull. The insulation will tear and will not damage the wire inside. Sometimes it helps to chafe the insulation a bit with the thumbnail before pulling. Be careful where the wire is being pulled from. It should be held by pinching with the other hand.
I never use a wire stripper, but dikes or wire cutters. The dikes must be very sharp. I don't use my dikes for anything except cutting wire, and I don't loan them, which keeps them in good shape.
Squeeze the wire slightly with the dikes at the point where the insulation should separate, then pull. The insulation will separate and slide off the end of the wire. The intent is for the dikes to cut through the insulation but not the wire, score the insulation, and allow it to tear the rest of the way off.
More care must be used with thinner wire. If stripping very thin wire, use fingernail clippers following the same procedure. However, nail clippers will not offer a "feel" and with them it's easy to cut too deep, cutting the wire. Clippers do offer precise control, however. With practice they work well.
Try not to score the wire when stripping. With multi-strand wire it's easy to cut some of the strands but leave others. Make a decision whether the wire is too damaged, needing to be redone. If being soldered, solder will flow up the wire a bit if done properly, strengthening it.
What I would do in your situation is make a custom wire stripper using fingernail clippers by placing a piece of metal between the cutting surfaces, preventing them from coming together completely. You can then reach into small spaces, squeeze, and pull off insulation easily.
Another method that works well is to roll the wire on a knife blade with your thumb, cutting the insulation completely around the wire, then slide off. For small wires this works well. It's not necessary to completely cut through the insulation, but score it all the way around. Doing this much will leave superficial cuts in your thumb, but it works well providing good control.