I recently inherited a 99 in 358 Winchester. It's in rough shape but I just got done cleaning the bore and it looks perfect. I may get it restored/ refinished but I think the bolt will need to be replaced. Are the bolts on these caliber specific? It's one that is jeweled. Or at least it used to be.
You will need to determine the year of manufacture. Also, don't be surprised if the new part doesn't just drop in. Savage 99s were hand fitted - at least the older ones were- so interchangable parts can take on a whole new meaning.
That said, what you want to do should be doable. 24hourcampfire has a very active Savage Collectors forum. Many on that site are experts and have lots of parts. They are very knowledgeable, helpful people. Good luck!