I'll be honest...many sword and knife makers do their hamon pieces on a grinder. They try and be as gentle as possible, and cool as often as needed. However, dipping a knife every pass on the grinder, and dipping a sword are two different animals. You are going to get the sword hotter.
The thick edge can be ground away on a grinder, as it is well below the hamon area ( hopefully).
What the togishi do is use water stones and lots of water. The rough grinding they do is on a huge slow turning wheel that is wet ( think 48" Tormek grinder). Once you learn to use the water stones, it is amazing how much metal you can remove in a very short time.
Easy.......NO!
Producing the best hamon.....YES!
If you use a grinder there are a few tips that will make the best outcome:
Use fresh belts. When it slows down, change it.
Use slow speed, and use light pressure.
Dip in water as often as possible.
Grind bare handed.
Once the basic shape is refined, switch to hand sanding.
Hand sand from 220 grit to 2500 at a minimum.
Read a bunch of tutorials on traditional sword polishing ( togi), and on hybrid sword polishing. Most peoples method will probably fall somewhere between the two.
When I get home ,tonight, I'll post a bunch of good links.