I'm not sure that a 250Kohm pot has enough resistance to completely silence the Guitar.

I know that single coil pick ups use 500Kohm pots - Strats.... etc
And double coil pick ups use 1000Kohm ( 1 megohm )
You might find a diagram @GuitarNuts.com
As for the hum - putting the strings on wouldn't help - but some metal component ( I suspect a pot body ) is not grounded