I leave the dead mosquitos outside as an offering for the local flying squids, much like ravens they are smart af, and a pleasant addition to the square concrete jungle we made for some reason.
Like spray them with water? Sure, if they're in the sink or on the counter. If you mean just swat them away, I wouldn't trust that to kill them. And as soon as it doesn't kill them, and they find their way back to the nest, there's a chance they'll lead others back, if they found so much as a scrap of food.
You know, I feel like I know that smell as well. Not anywhere NEAR as pungent as the ant smell, but I've been in some... Unfortunate situations with enough roaches that I can conjure up that smell.