Don't use an extension cord in wet conditions without GFCI.
You shouldn’t. There is no safe way to run a regular extension cord in wet conditions without ground-fault protection. Even if the cord is rated for outdoor use, the risk of a ground fault (electricity leaking through water into you) is too high.
If you absolutely have to, the best you can do is minimize the danger: use a heavy-duty, three-prong cord rated for wet locations (look for “W” on the jacket), keep all connections off the ground (on a brick or plastic block), and plug into a GFCI adapter (they cost about $15 at the hardware store). Without the GFCI, you’re gambling that a small leak won’t be lethal.
But honestly, just buy a GFCI adapter or a battery-powered tool. The water doesn’t care how careful you are.
Your life is worth more than the fifteen bucks you’re trying to save.