I've done some hand grinding of carbide with natural diamond wheels. But I use a 6" bench grinder, using the same technique as I would use for grinding HSS drills. Shars Tool offers diamond wheels on a budget, and I find no problem with using them. I would recommend making an integral rear flange/bushing combo to adapt the wheel to the motor shaft, rather than relying on the crappy little flanges that come with cheap bench grinders. A true running flange will make a true running wheel, and it should not 'bang' your carbide enough to damage it. I like about 100 grit. It cuts carbide easily without leaning hard on it, or dwelling indeterminantly while you wait for it to wear its way across the face, such as green wheels do.
I only use a green wheel for backing off the steel support under brazed on carbides. I usually grind a little excessive secondary clearance across the tool, the go to the diamond for actually sharpening the primary clearance angle, which supports the cutting edge.
As for using your Drill Doctor, I do not know about that, but I understand that they only have a small diameter wheel in them, and if they are CBN, then it may not seem so sharp next time when you go to grind HSS with it.
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)