Why do old toggle switch leads read 40VAC?
Yes, a new 15A-120VAC switch will certainly work in a lower-voltage application.

Regarding the voltage across the switch leads, 40VAC is a very mysterious reading. Could the current actually be DC (for a thermostat perhaps)? I'd want to figure out what the switch was supposed to control:


Visually trace the wiring from the switch, if possible
Are the wires normal 12 or 14-gauge thickness? If so, it's probably supposed to be a light or outlet switch.
Can you isolate the circuit by process of elimination? Are there other lights or receptacles on the same circuit that can give you a clue about what this switch is for?
How many wires are available in the switch box? If there are only two, then check the voltage of each against ground. One should be 120VAC (supply) and one unenergized.
You can check your hypothesis that the old switch was broken by testing for continuity in the switch's ON state.


It's entirely possible that this switch is wired to a circuit that is no longer useful, or perhaps that the wires aren't actually connected to anything and what your meter is picking up is an induced electrical current due to current in adjacent cables. Without determining what this switch was originally intended for, it will be hard to explain the voltage reading, and hard to know whether the old switch was broken, or whether the wiring was disconnected.