The Deus-Ex games are good for this. Haven't played the originals, but the modern games let you use a silenced pistol for most of the game.

If you want more shooting, take a look at Rainbow Six: Vegas games (1 & 2). It's a squad-based tactical shooter that focuses on info gathering and setup more than flinch reactions. You can choose to use a silenced pistol for the whole game if you want. Most levels are stealth-based until you are caught, though there are some full-on shooting sections.