Would using a coax switch with one side connected to ground or nothing, do anything for lightening protection or would it just cross over inside the switch..?

HI Coyote,
. Your best bet is to disconnect the wire outside the house and ground it outside. It would jump across the inside of the switch since it just jumped miles in the air. I got lucky once, while I had the radio disconnected from the tuner, the antenna was still connected. There was a near by lighting hit and I heard a pop inside the tuner, luckily no damage. If the radio had been connected the front end would have been toast.
73,
Rob

It will also jump inside the coax. A few millimetres of dielectric isn't going to influence a bolt or even a high voltage RF spike. That is the reason you don't really need to ground the inner conductor if the shield is grounded and IMO if the coax comes down the mast and the mast is metal and the mast is grounded and a bolt hits the antenna, it will find the grounded mast and the ground attached to the mast even if the shield is not grounded, IMO

this is not lightning protection advice and I am not an expert,  dont try this at home, wear a helmet, life is dangerous.