I'm sure there are guys here that have done what you're thinking...me included. I've taken a number of bowls down and restrained them, etc. If you have a buffing wheel (felt wheel on a grinder motor, etc. is fine) can do it fine.
Procedure: Start out with the attitude that the pipe is going to dictate the end result. If you go in with a strong desire for one specific outcome you'll likely be disappointed. Be prepared to appreciate and enjoy however it turns out.
1. Sand wood down past external stain, etc. (220 - 320 - 400 - 600 - 0000 Steel Wool)
2. Apply stain. Do test patches on spare briar chunks for color testing. Use Fiebings leather dye or similar (Lincoln is OK) or waterproof drawing inks (I've used forestry green and red with very good results). Let the stain dry overnight.
3. Sand with 320 or 400 until desired level of stain vs. grain shows.
4. For two tone stain apply darker color first...dark brown, black, etc. then sand down til dark color is present on grain and you have dark stain sanded off 'background'. Let it dry overnight. Then apply lighter or brighter color and sand as in #3 above.
Note: I've used dark brown with green, dark brown brown with orange, black with red, black with reddish brown (mahogany), etc. All look good. This is art part so you can't go wrong, really.
5. Sand lightly with 400 or above grits to your preference ending up with 0000 Steel Wool taking care to not remove too much more stain.
6. Carefully buff on a clean soft rag or felt wheel with a very light load of white diamond or similar white compound.
7. Buff with a wheel dedicated to Carnuba if wax if desired.
Note: Wax is not required, but must be applied with a wheel of sufficient speed so that the friction melts the wax. Carnuba is very hard and needs a fast wheel. I've used a Dremel many times with good success... the secret with a Dremel is to keep the wheel moving lightly and quickly on the surface in the same kind of motion you would use in shading with a pencil on paper. Practice on scraps to get the right feel for it.
8. The level of surface shine you end up with is rather dependent on how high the grit of your final sanding is, I think. Some guys go into the high number grits like 1200, etc. I go to 600 or 800 tops, then the Steel Wool. But I don't like it to look like I put a coat of high gloss varnish on it, preferring a softer finish.
That's it. It's not hard, but you need the proper materials and tools. A drill will not work for this at all! You need a Dremel or a buffer/grinding motor!
If you don't want to do it, I would do it for you...pay me in tobacco...Gawith Dark Flake Scented...8 oz.! Or some such barter. Your choice of color(s).
PS: the stem, if ebonite (etc.) looks oxidized. I could also clean that up.