Can you slide the winch towards the front of the trailer so that you can crank it with the shield still in place? If so, then a hole in the shield to run the cable through, and a rubber bellows to seal around the cable might do it. Pop a big screw eye in the deck to hook the cable to when not in use.
I was gonna say that your wench sounded a little inflexible about the whole thing, putting you on a spending embargo, but given that you're talking about replacing her with an electric model I understand her point of view. (Apologies, I was raised by a grammar nazi and have low self control).