BigE3 nailed it. Those are definitely not the original grips, it came with what Smith called diamond magnas (wood with the s&w medallions). They might be Bakelite imitation stag grips, very popular in the 50s.

The finish looks in really great shape for a gun of that vintage that no doubt spent some time in the holster. Perfectly safe to shoot with standard pressure ammo by the way and probably very fun too.