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In the recent "Ask the Devs" video, one of the questions was "why does Hunter's crossbow not have a cooldown?"
I think it could have a cooldown similar to Redeye and Rhino. It would basically have infinite usage like Redeye, but it would have a sort of overheat like Rhino. So if you just continuously spam the shots, it will reach an eventual cooldown, but as soon as the cooldown begins to reverse (like Redeye; don't know why I can't think of a word better than "reverse") you can fire again. Also, using the EMP bolt and actually disabling something will reduce the cooldown on the crossbow.
Think of it like Doomfist's hand shotgun from Overwatch, if you've played that.
Just an idea.