Why would using a 240V tool on a damp day risk electrocution?
It rather depends on the setup supplying the 110V equipment as to the electrocution risk.
Many/all commercial site supplies have centre tapped 110volt transformer so the voltage to ground is 55v so the chance of death while not zero is low.
So if you are using a centre tapped 110volt transformer (most likely as site transformers are common) your risk is low.
if you are using a different transformer (common for inexpensive 240v -> 110v step down ones) the chances are higher As you get the full 110v to ground.
If using a 240v supply your chances are higher still.
Add damp to the mix and that elevates the risks by a lot. You can increase it again by using one hand on the tool and the other on the item, this gives a hand to hand path transiting the heart a few milliamps (at 240v) usually over 30 can stop your heart or put it into fibrillation so providing a death opportunity