Dunright, Welcome aboard. Sounds like you have a first year production 99F. That model was introduced in 1955. They did away with the "1899" nomenclature years and years before that.
I have a 1957 99F and the grip cap looks a whole like the same one they used on the Savage Fox shotguns. If this is sized about right for your rifle, it'll do you close enough. (Get a screw too).
http://vintagegungrips.net/ao-s97.htmlAlso, Lightfoot who carries some Savage parts, may be able to match you up with something original. If he doesn't weigh in here, send him a query via a PM.
Edited: Whoops I was beat to the reply