Soldering an AC power cable
Are you going to have the AC jack (power entry module) on your new back plate?  If so, what kind of terminals does it have on the inner side?  A photo or a pencil sketch of your new back plate could help us visualize the problem.

Without knowing anything else, I would recommend splicing the wires with a crimped butt terminal (like this one or this one).  It's a thin-wall metal tube inside of an insulating plastic tube.  Each end of the tube can be crimped onto a wire.  Here in the US, you can get them in any hardware store.  Crimped connections are less brittle, compared to soldering.

Splicing plus soldering works too.  Heat shrink is a more reliable insulation than tape.