You'd ideally want to strip out the wiring that is corroded, or you'll end up with ongoing issues.
Unless you can clean it up with wire wool or something?
Immobilisers aren't too complicated to eliminate, follow the generic black wires back and you'll see it joins into the bikes wiring loom somewhere.
There will be 2 wires from the immobiliser, note the colour of the wires they are tapped into (in the bikes wiring loom), cut out the immobiliser wiring and solder the original bike wires back together.
If you want to retain an immobiliser, you'll want to note the location where the immobiliser wires tapped into, and use that same location to solder in the replacement immobiliser.
I stripped out a complete Datatool alarm system+immobiliser on my previous bike, that had badly corroded inside the Datatool control box.
It was tapped into 2 positions in the bikes wiring loom. The bike ran perfectly afterwards, with loom wires soldered back together.