I need to cut out the existing wire and splice on new wire since the insulation is torn up beyond repair (shorted out the 5A fuse) , obviously a Temp repair until the part can be ordered
I would use an 18AWG multi-rated TFFN/AWM/MTW here
The most commonly available wire that I can reasonably say is usable for this application would be an 18AWG wire that is multi-rated as TFFN (fixture wire), AWM (appliance wiring material), and MTW (machine tool wire). This wire is generally a stranded copper, with PVC insulation rated for 105°C in appliance (AWM) applications, and should be available from any competent electrical supply house (as it's also used for internal wiring in light fixtures, hence the name "fixture wire").
UL 486 listed wirenuts or insulated butt crimp splices suitable for connecting 18AWG to 20AWG (the latter applied using an appropriate crimp tool) should be used to splice the patch-wire into the float switch wiring, by the way. You are correct, though, that the low-voltage fuses used on HVAC control boards are typically of an ATO (automotive) type (rated for 32VDC/VAC), so replacing the fuse with a plug-in automotive type of the same amp rating will work.