You could just have 3x volume pots, no tone, so you select the pickups via the volume pots. But then you run into problems with parallel pot resistances to ground, so you’s probably need 500k pots for the single coil and a 1Meg for the humbucker.

It won’t be quick changing pickups for live work though, so not an option I’d recommend. Though if you had each pot a push/push pot you could have individual pickup selection via those., which would be a lot quicker.