I've turned the end cap and buttons for a friend who has made powder horns with them. The horn is hollow with a solid tip. The solid tips might be 3 or 4" long, but tapers to a small diameter on a curve -- much like the tip of a deer antler. Depending on where you cut it off, the larger diameter might be 5/8" or so. A sierra blank might be possible from one -- I think I have a tip around here that I can measure later today.
If you find a full horn, insert a metal coat hanger to measure down the hollow to the solid part, and transfer that measurement to the outside of the horn and mark it where you want to cut it. Use a hack saw, the prep the blank like you would antler for turning. It smells bad -- not like antler, or your worst nightmare at the dentist, more like bad foot odor. It will take a great shine, and if you find one with nice color variation, I'm sure it will add more character than a plain black one.
Edited to add photo and measurements:
This tip is 4" long, and about 7/8" at the cut end. At 2.5" from the cut end, the diameter is 1/2".