I personally would not use a corded electric mower in the conditions you describe. However, the risk of electric-shock can be reduced if you are using a three conductor, grounded, extension cord, plugged into a GFIC outlet, that has been tested, and is known to be working. In your situation, I would be using a different type of mower, either gas-powered, or battery powered, to cut the grass.

+1 or ericwi's answer. Also, I suspect the mower is never going to cut correctly with so much wet grass getting balled up under the deck.

I'd just suck it up and wait for the ground to dry a bit, and then go over the grass twice -- once with the wheels as high as they'll go, and then again (maybe after raking) to make the grass a bit neater and shorter.

BZZZZZTTT!! "Guess i should have bought the gasoline powered machine! But, at least, i have a nice puffy cloud on which to loll around on, watching and waiting fer my dear wife to get electrocuted by the same mower!"

Buy an extension cord plug with a GFCI built into it. Then you can use it anywhere.

Here is a link that might be useful: Link

let the ground dry out