Return to Castle Wolfenstein

I’m in mission 6, part 2. I just got out of the wine cellar, killed the guard upstairs without making a sound, and saved. I opened the door, and got spotted by two guards, who shot at me. Then someone else within earshot set off the alarm, costing me the mission.

Everyone says to use the Snooper here, but I ran out of ammo for it. Is there any other way to get past those two, or do I have to resort to ammo codes?