I have some Bose headphones but the cable has become damaged. How easy would it be to replace the cable? I have some spare apple ones which I can use the cable, volume control etc from and a soldiering iron. With a bit of shrink wrap to tidy up after?

Well, you’ve probably not got much to lose, most often once the internal wire breaks you’re stuffed, but if you’re prepared to chuck them out anyway, it might be worth giving it a go.
I’ve got a pair of Etymotic ER6i’s, which have a break in the cable somewhere, which is a particular pain because they weren’t cheap in the first place, and I forked out another £100 on custom eartips for them!
It is possible to retrofit the cable and remote from a pair of Apple earphones, but they’re susceptible to the cable breaking near the plug anyway.
What I’d like is a short length of cable on each earpiece with an MMCX socket on, so I could use easily replaced cables from the likes of MeeAudio, who do a Bluetooth cable for that fitting. How feasible that might be, I don’t know, I do know it’s beyond my meagre skilz.

I can’t comment on that particular set. The last pair I did though,

On the upside, soldering three or four wires is trivial.

On the downside, the headphone wiring seemed to be made out of butterfly wings.

On the downside, the headphone wiring seemed to be made out of butterfly wings.

Yeah, which is why machines do the soldering… 🙁

The only to watch for is if the wire is enameled – which it often is on headphones. A decent soldering iron should get hot enough to burn off the enamel when you tin the wires. If you have trouble getting the solder to stick, burn the enamel off with a lighter or small torch first.