Where's the switch? The wires should be attached to a cylindrical "push button" switch that connects the two wires together when the clutch is disengaged... as far as I know all Hondas switch ground so at least the wires can't blow a fuse by touching metal.
The switch goes in from the lever side so it won't be pushed out by the lever or pulled out from the cable side. Remove the clutch lever and it should push out using a screwdriver or blunt tool. Possibly you can solder those wires back onto the switch terminals and have a working switch again.
Or just jumper the switch wires and remember not to start the engine in gear without disengaging the clutch.
Assuming this is a K4, the starter should work when the engine is in neutral. There are two ways Honda enabled the starter when either in neutral or with clutch disengaged (or both) - either an SSU, a somewhat complicated electronic module, or a simple diode from the neutral switch to the solenoid ground (the diode is to isolate the neutral light from the clutch switch so it isn't on whenever the clutch is disengaged). I don't know which they used on a K4. The clutch switch directly enables the starter either way, and it's nice to be able to start an engine stalled in gear as the transmission is not often cooperative when asked to shift gears on a stopped engine.
The SSU is too complicated to try and explain, a failure can disable the neutral start capability but with the clutch lever pulled it should still run the starter. Same with the diode but it's very simple (and easy + cheap to replace) - failure will either disable neutral only starting (diode failed open) or have that neutral light activated by both the neutral switch and the clutch lever (diode failed short).