That depends on their orders. If numbers is not the mission, you don't shoot for body count. You shoot whatever gets your mission done. If your mission is recon as a sniper, you recon, label targets, possibly take a shot of opportunity, but you get the intel to your superiors over body count. If you are sent to locate the commanding officer of a base, and you can't locate him, you create a situation were he shows himself, by messing with them. If your orders say to cause problems, then you cause problems. Problems could be dead soldier or stressed out soldiers.
In Vietnam, there were instances were one was not in a position to kill the other side due to pilitical situations. Such as the mentioned shots across the border into Cambodia. The US was not at war or even in conflict with Cambodia until the middle of 1970. They could not legally go in there and kill North Vietnamese (or other allied Communist forces). So instead of kill shots, the idea was to scare them as much as possible. Psychological warfare was used heavily and that included snipers. Maybe it was more a Navy thing than a Army thing.
The Dominion (Vorta and Founders as well as the Cardassians at times) liked using psychological warfare as well as direct combat. The Houdini fits their methods properly.
Regardless, this has basically nothing to do with security officers on the Enterprise...any Enterprise.