I've considered doing that too but for the life of me I just can't crawl under my 2800# cutter...I think it has something to do with all I've seen in the last 40 years of police work..
Know exactly what you mean. My 3008 Bush Hog weighs around 2000 lbs and I wouldn't think of crawling under it without some safety/backup. That's why I prop the rear two corners with a couple of 2"X6" cut to length and drop the lift so some weight rests on props. I've heard of folks running the tractor and cutter up on a trailer and sharpening the blades.
If you have a pull type hitch maybe you could back the cutter wheels onto the trailer and sharpen. I'd still put blocks under it for safety measure in any case.