i change my cables before they break.
around here, there are a selection of sizes and types of sticks,
and i have my swiss army knife to custom size one.
I'd advise Maple, if handy.
Alder is too oily, fresh... ok if it's older alder.
Fir has too much pitch.
and Chittum is the source of the original Ex-Lax, so avoid it at all cost.
Elderberry is hollow, so it's a no-go.
cedar might be ok, if well aged.
gene has a wood problem, i guess.
a stick or wrench could also be used to loop and twist a section of the cable, once the broken end is secured.. use the tape to then secure the twister and loop......
a million solutions to a problem that should have been prevented.
i've watched an inner tube get wrapped with E-tape, then re-installed and aired up... it got that bike back to camp.