Note that both weapons use darts.
The problem with firing underwater is not the propellant (I suspect that humans are sufficiently imaginative to protect even black powder from water long enough to fire).
The problem is that the round must wade through the water (much denser than air) which is constantly slowing it, and must first get rid of the (non-compressable) water in the barrel of the weapon to even begin its journey. I suspect that a barrel full of water is only slightly more dangerous to the shooter than a barrel half-filled with mud.
A weapon that fired the round without a barrel would only have to contend with the enormous drag of the water on the way to the target, but I doubt that it would be very accurate.
For a true “handgun” to be used reliably under water, I would think you’d need to continuously pump air into the barrel before firing. (Your range would still be extremely short. Anecdotal evidence suggests that a rifle or machine gun fired into the water loses its effectiveness within a couple of feet of the surface.)