Savage rifles are fine with copper jacketed bullets, that's what they were designed for. Just load them to velocities in use at the time and don't try to hot rod them. Hornady likes to list hot loads in their manual, for example.

“The Savage 99 Pocket Reference”.
All models and variations of 1895’s, 1899’s and 99’s covered.
Also dates, checkering, engraving.. Find at www.savagelevers.com