Ron, IMHO, the TPT, or the HHT, will not degrade the edge. As for the TNT, I've seen many barbers I spoke with use it on their own razors when I spoke with them about them.
I haven't experimented with doing a TNT with a shave ready blade, and then shave. A barber I asked said that nails and hair are made of the same thing. Hence the TNT shouldn't hurt the edge if done with the weight of the blade. Dunno, and I'm not curious enough to shave with one to find out. :D