The pipe making demonstrators at the Pipestone National Monument use nothing but wood working tools on the pipes they make for exhibit. That includes using a brace and bit to drill the holes. They work red pipestone, but soap stone being very close in carvability, I'd imagine you could do all the work you need to do with just wood working tools and sandpaper. I think this is true as I saw some two-toned pipes there made of red stone and black soap stone combined. Woodcraft Supply used to sell soapstone for carving, and I'm pretty sure they meant it to be carved with wood working tools, as that's their primary business.
The pipemakers at the National Monument did all their work freehand, no vises or clamps or patterns, just by hand and by eye.
I have both some black soapstone and red pipestone here and tested the soapstone with a rasp, it seems to cut about like the red stuff. I still haven't made anything out of it, so can't testify to it's working qualities in detail.