Cut Out Switch does not work?

I have Flymo XLT2500 Multi-tool.

I caught the cable between the On/Off switch on the handle and the engine on a branch and managed to snap it at a small connector. I've tried soldering the ends of the wires together but the cut-out switch does not work now and to turn off the engine I have to disconnect the spark plug.

I've thought about unscrewing and removing the casing from around the engine to see whether the wire is broken somewhere else but I'm worried that half the engine will fall out.

There are a number of options:
- Can I re-connect the wire and if so how? Soldering does not seem to work
- How easy is it to replace the wire assembly? If it is relatively easy is there any advice on how to go about it?

Thanks.

T4