Weapons that have an "Active Time" (like the Raptor or the Turbo) should remain in your inventory while active (shield excepting), but things that you just fire and are done with (EMP, Scorpion, etc) should disappear immediately.
Perhaps for the Assassin leave it so it appears as "Active" until it's fully locked on, then have it disappear.
As soon as any "Active Time" ends though the powerup should be gone, or at least fade out a lot faster than it does. I haven't actually clocked it, but it feels like it's a full second, if not longer, and that's a lot of time in GRIP.
Desktop: i5-3570k @ 4.6GHz, RX 480 8GB, 32GB DDR3-1600, Win 10 Pro
Laptop: i7-4720HQ @ 2.6GHz, GTX970m 6GB, 16GB DDR3-1600, Win 10 Home
Currently Playing: Gravity Rush 2, GRIP, Guilty Gear Xrd -REVELATOR- | http://i.imgur.com/FuDx2Un.jpg