Actually, this is exactly the reason I recommended the "g-string" Decimator. Unlike a lot of noise-gates (such as the "normal" Decimator, that I actually have) the "g-string" has a loop, so that it can sense the level at one point in the chain and open/close the gate in another point. So the OP will connect the "input" (level-sensing part) before the compressor, and the send/return (actual gate) after the compressor.
I agree that eliminating the source of the noise, is always the best option, but I suspect that any compressor will have some hiss with extreme settings, and it looks like the OP can actually be served well by a noise-gate because it looks like this is the actual effect he's trying to achieve (distinct on/off sound with no dynamics).
Thanks man. I'd always wondered what the difference was between the two Decimators, even visited the website a long time ago and wasn't clear on the difference. Just checked the website, and it's still not clear (to me) what the difference is when reading the website copy.