It's not exactly a pistol round, Catfish. In point of fact, it's closer to the 7.62x39mm round used by the Soviets in the SKS and AK-47 than anything else.
The 7.92x33mm Kurz actually looks pretty interesting to me by itself. But if one just has to monkey with it (and someone must, because that's what we do, right?), it could be an interesting platform for taking up to .35 caliber to lob .357" pistol bullets or even .358" rifle bullets, though you may not get the velocity to expand the rifle bullets. Probably have the same problem going to .338" bullets, too, I'd think.
Now, going down, .30 caliber is an obvious choice. Plenty of guys out there are using the .30-30 Winchester to push a 125 - 130 grain bullet to just over 2000 FPS and taking deer and the like out of 10" to 14" Contenders. No reason the 7.92x33 Kurz can't do the same thing. The German round is actually specced for about 2250 FPS out of a 16.5" barrel. Give it a 20" barrel to pick up more velocity and you might even get enough velocity out of 150 grain bullets to use them at sub 200 yard ranges.
Taking it down to 6.5mm with a 20" barrel could give you something on the performance of the 6.5 Carcano, only without having to worry about the bolt getting implanted in your forehead, and out of a significantly shorter action (not that the 6.5x52mm required a terribly long action).
Might be an interesting platform to build from to go all the way down to .22 cal and 6mm, even. The PPC cartridges were built off of the .220 Russian, which itself was based on the 7.62x39. Could be a wildly accurate BR cartridge.