Picked up a straight razor -- Razor Emporium's "Try" kit. (You can't go too far wrong for $70USD, I reckon, and while it's a cheap-ass Chinese Gold Dollar razor, their in-house technician-sharpener gives it the treatment and a new handle.)
There was blood. I did the part under my nose, and cleaning up the edges, with my normal safety razor.
But that has to be the smoooooothest I've felt my cheeks since before puberty. Real smooth. And, to be fair, there was some amount of blood on a daily basis when I was learning how to use my safety razor. Might have to continue with this.