I haven't carried while mowing, but I have dispatched a few snakes around the yard and pond.
If was going to carry while mowing, I have a Smith & Wesson Model 60 stainless that I would load with shot cartridges. Its very small and does the job out to about 20 yards. I would have to carry the stainless. In summer, I would ruin a blued gun with sweat.
Even a .22 with shot will do OK. You just have to get closer. With a handgun and shot cartridges, the shorter the barrel the better.
The Model 60 is a great gun but I would doubt my ability to make an effective shot on a snakes head from 60 feet, even with a .38 shot cartridge, but I really don't have much experience with them. I used to load the Ruger with shot but it isn't terribly effective, even at close range. I just load it with long rifle hollow points now and it's good for most anything that I'm liable to encounter while mowing. I can hit a snake in the head from 15 or 20 feet without a problem.
You are absolutely correct about the short barrel. Many people don't believe that but it's true.