Andy S,
Well, it needn't be choc blocks. If physically possible (in the sense that there's enough spare wire) a lump of wood with woodscrews through the connectors which need to be mated would work, though the screws shouldn't stick out of the back of the wood in case of -zap!-
I suppose that' would be breadboard construction at its simplest.
But from the photos, it looks like only one connection has blown. The rest of the discolouration may just be magic smoke condensate. Try connecting the loose red wire to the wire it mates with and leave all other connections in place. Maybe use a short screw and nut through the two connectors, and plentiful insulating tape.
Andy