Randall Styx says:

A. Get a wire stripper that has an option for finer wire.
B. Get a nice sharp wire cutter and gently cut just into the insulation and pull. The cut in the insulation will start a tear in the insulation that will run through the rest of the insulation as you pull.
C. Depending on how your teeth are aligned, bite into the insulation and pull. You’d be accomplishing the same as B, but with duller cutters. (You don’t have to swallow the piece of insulation that comes off.)
D. Cut into the insulation with a sharp pocket or hobby knife and pull. You can cut into the insulation on multiple sides.
E. Shave the insulation off with a sharp knife like you might sharpen a pencil.
F. I don’t have a True Track switch in front of me, but examine it. You might be able to replace all the finer wire and go directly to the connection points on the switch machine with the wire from the controller.
G. Get some connectors that don’t require stripping (like those commonly used to add trailer wiring to the tail light circuits of an automobile).
H. Get a “push in” connector bar from an electronics store (also does not require stripping) or cannibalize an old computer or stereo.
I. Bend 1/16 inch of the wire back on itself to form a hook. Make a hook in the controller wire, Engage the hooks and solder. Cover the joint with electrician’s tape.
J. Grab both wires with an unpainted jaw or pincer type paper clip. The clip will become part of the circuit.
K.Slice the wire lengthwise with a sharp hobby knife, starting where you want the wire to be bare and cutting toward the end of the wire. Fold the insulation back to bare the wire.