When I have sharpened shovels and other digging tools, I use a grinder with a fine grit - carefully. It is quite easy to draw the temper if you get too eager. I imagine a Dremel would work OK as well - just take it easy. Nothing wrong with a file for that matter - it will simply take a bit longer.

Let us know if you are able to shave with your shovel. I have never accomplished that.