It
might be doable, but at pretty high risk of messing up either the grind or the HT. You'd be doing something pretty unique, with likely some kind of completely custom setup, and few people will be qualified to give you
good advice. You'd be best served to take your question over to the shop talk forum and ask there.
However, I suspect you'll get the same advice as you have here. I personally think a grinding wheel is a terrible idea, especially if you're doing the stock removal by hand. It's just asking for an accident. Good luck!
BTW, here's a couple pics of what I
still think you might want to consider instead, the Battle Guard:
Basically a full-flat ground Battle Rat with a guard.
Perfect pig sticker IMO! (Especially with my re-worked tip.)
Let us know how it goes. If you're really serious about wanting only 4mm thickness, you might almost want to consider some kitchen knives at that point.
PS - The Battle Guard feels VERY light and fast in-hand (yes, that's mine in the pics). The flat grind and guard serve to pull the balance point much further aft than the Battle Rat, and it still weighs a bit less than a BR. The flat-ground Satin Battle Rat (SBR) is 1.5oz lighter than the BR at 15oz versus 16.5oz. I wouldn't call any of them heavy knives for their size.