I have put catfish in the bed of my truck, driven home afte a night of fishing and cleaned them in the driveway and all of them still moving like they were just caught. I had 1 catfish that was still alive after 4 hours in my truck and his mouth was still moving after I reteived my filets.. These are hardy fish and I would say, put them on a stringer and filet them at home. As far as dragging filets around in dirty water.....Why would you do that?... Cut out the filet and put them in a ziplock bag before you head home..
On a side note.. I have been camping and caught fish/ cleaned them in the same water I caught them from and fried them right there on the bank.. As far as washing or soaking them in muddy water, I think thats a bad idea. Rinse them and fry them is okay