Looks to me like all that melted is the plastic loom material they use to dress the wiring up.
The switches can normally be replaced without losing any charge. But I would recommend finding the service manual for the chassis your working on.
The only way to test the switch is to remove it and apply the specified pressures to see if it opens and closes at the appropriate pressures. You can jumper between the two wires to see if the compressor clutch engages - but all that tells you is either the switch is bad or your low on refrigerant (I would suspect the latter before the former, but if you let the compressor run for 2-3 minutes, if the unit isnít cooling then youíll know itís likely because itís low on refrigerant).
For the switch PSI ratings, find a switch with the same or higher cut-out (low) PSI, and the same or lower cut-in (high) PSI. But it surprises me that there isnít a cross reference replacement for your chassis.