Lapping 2 cable ends together and then wrapping with thin copper wire (striped from electrical cable) then silver solder is one method. I would make the overlap 1 inch.

another option is to find some small copper or brass tubing (made by K&S), slip the cables in from either end and crimp

both methods are simular to what we used to do to make flying lines for control line model airplanes. The crimped connections used to be good for 40+ lbs of pull and the soldered connections sometimes are above the breaking strength of the wires.