I shoot the Cyclone, among others, largely becsue it's relatively fast (355fps). You can spend a lot of time and energy trying to silence a crossbow and end up frustrated. That's largely because the sting is propelled so much faster than a vert. bow. String 'silencers' and limb savers will do very little in the way of dampening noise. Vibration, perhaps a little, not noise. What they do do is decrease the speed of the string, ergo the arrow. Aside from slowing the string, you could try filling the hollows in the stock with foam, etc.But even that won't do much to reduce noise. NOTHING, absolutley nothing, can be done to reduce the noise to the point that a deer won't hear it. And since noise travels much faster than an arrow, it's part of the "advantage" of using a crossbow.
I've finally come to the conclusion that speed of arrow is at least a partial answer to preventing deer jumping the string.(Get to 'em before they react). Next is keeping shooting distance reasonable (40 yard or less, shorter with slower bow) and, last, don't shoot until the target animal is relaex, not poised for flight.
You'll get used to it in time. Not that big of a deal anyway, you're highly unlikely to be able to recock the bow and shoot again if you do miss. One big reson why I like single shot rifles, handguns and now crossbows: One shot is that much more challenging. Made me a better hunter. Enjoy.