I use the following hand and power tools for making sayas:
Band saw for splitting wood, cutting out a profile ( I do it after glue-up)
6x48" sander for rough flattening, rough-sanding, distal taper forming
Granite plate for precise flattening
Saya chisels for carving
Drill press for pin hole drilling
Bessey clamps for gluing
TD-90 for grinding to shape and rough finishing
Final hand-sanding and oil/shellac finishing
The Process
I typically let re-sawn wood sit for a couple of days, to release tension, then flat-sand glue-up sides, carve a cavity on one side, glue the halves together, profile, form a distal taper and bevels, and then shape it. Some woods I finish with tung oil and shellac and some with natural oil/wax blend.
M
PS: with sharp chisels, you have a better control and a better result. As Devin and Mario can attest, I can carve a cavity in 10-30 min on most woods. Some woods like burls are trickier, but sharp chisels will do. You might have some tear-our, but not too much, as long as you are "shaving" the surface with chisels, and removing a little material at a time. It's important to carve with the grain, though sometimes the grain on burls is all over the place and sometimes I carve against the grain to get a better grain figure on the saya.
Router would be faster, but you won't be able to remove the material to mirror the blade geometry for a tight fit. I made a few sayas from walnut burls and even red wood burl. Didn't hear any complains about twists or shrinkage. On a red wood saya I ground tip area too thin, so it chipped off on a burl figure, so it is for a re-make. Red wood is pretty brittle and have to be left a little thicker.