My wife bought a Dremel to file the dogs nails down. One night, while having a lot of beverages, I decided to sharpen my machete and hatchet with great results. Is it okay to use on a mulching blade without it messing with the aerodynamics? At which point do I stop and just buy new blades? I have a Honda HRX with dual blade mulching.
I also have a Honda mulching mower (walk behind), and use a belt sander to sharpen my blades - clamp it down to a portable work bench and sand away. It works great, only takes a couple minutes, and doesn't change the aerodynamics. I touch it up with a file to remove the burr if needed.
I took my blades to a local shop once to get the blades sharpened, thinking they'd have a jig to put it in for grinding to a factory edge, and when I got them back they looked worse than when I'd used a circular grinder. Turns out they don't have a jig - just do it by hand on a grinder. They charge $25, and you can buy new Honda blades for the same price on Amazon.
To answer your question, the Dremel would probably work OK but would be slower than a best sander, and not as accurate. I sharpen mine two or three times a year.
No matter how you do it, check the balance after you're done so you don't get vibrations (hang it on a nail through the central hole and making sure it hangs level).