[BrianG]

I wouldn't do it. For one thing, only the last little bit of the wire is solderable. If you cut that off, you won't easily be able to solder to what is left.

There is an insulative varnish coating on the wire you'd need to remove if you do cut them. There are solvents you can use to do this, but be careful to not let the solvent wick along the wire into the coils area.