I've got to wonder what kind of "buffalo horn" you have. If you bought blanks from a knifemaker supply etc, it is most likely water buffalo. Water buffalo horn and bison horn work differently. What I'm seeing as potential hangups, based on my experiments so far:
I don't think you'll get significant penetration. By that, I mean that I don't think the stabilizer will penetrate through-and-through the horn. You will get penetration in any areas of porosity, or where there are flaws (even hidden flaws). From that perspective, stabilization is a good thing. Surface penetration will also drastically reduce the chance of damage due to insects. I think--not sure on this, as I'm not familiar with "Cactus Juice"--you'll also gain some protection from damage due to UV. It may also harden the surface to protect against scratching (not sure about that on something like pistol stocks).
Whatever type of horn it is, you may have trouble with the temps when you go to heat catalyze the stabilizer. This could be limited to dimensional changes (some minor warping), to cracks or de-lamination, to color changes.
My experiments have been with bison horn, which has a typical way of "scaling" as it dries and is exposed to sunlight. You get some color change, often some de-lamination, and cracking (which may or may not be structural). You don't see this the same way with horn from water buffalo. (I've had a chunk of water buffalo horn sitting on my bench for 20 years that other than scratches and some pre-existing insect damage, has shown little change. Bison horn would show much more damage/decomp.)
What I've seen so far has been that, across the board no matter what stabilizer I try, I get the best penetration on scraped surfaces. Sanding seems to seal or fill the pores, inhibiting penetration. Since I'm using a hacked-together setup, I'm not sure how much vacuum I'm pulling: enough to get 1/4" penetration of hard maple overnight, whatever that corresponds to. In 48 hours, I get what seems to be about 1/32-1/16" penetration on bison horn (plus all the flaws/checks/etc).
I've been shaping the horn close to final dimensions, roughly out any detail carving and the like, and fitting it in any critical areas like to a grip frame or similar. Then I'm giving it 48 hours in the vac using JB Weld's "Wood Restore Liquid Hardener" as the stabilizer. Then I remove it, wipe the surfaces, and let it harden for about a week at 70+ degrees F: no additional heat is needed to catalyze the stabilizer. Then I bring it to final dimensions, finish the carving, etc. In theory, if I had any areas that were exposed that didn't appear to be stabilized, I'd treat it again but that hasn't been needed yet. Then polish and finish out the project.
Test pieces done this way have stood up to a weather etc for up to a year without the scaling etc I'd expect to see with untreated bison horn in similar conditions. I don't have results on this treatment past a year, so can't say what to expect past that.