One of our people contacted the Daisy company about the CO2 cartreges, and found that they contain liquid CO2 at 900 psi. The guns that use external tanks at higher pressures, likely have a regulator, or a plenum chamber to bring the high tank pressures down to something more modest.
Muzzle velocity will not be proportional to chamber pressure. You can drop a lot of pressure before losing very much velocity. Barrel length and valve dynamics figure heavily into this too. Hand pump guns will be working below 900 psi, generally.
Pressure in the barrel can be approximated by using F=MA, where M is the mass (not weight) of the projectile, and A needs to be calculated based on 0 to muzzle velocity in (length of barrel). X = 1/2 At^2, V = At, solve for A
Solve for F and divide by the cross-sectional area of the projectile to get PSI in the barrel. Max P in the barrel will be a bit higher than this, as pressure drops off as the projectile goes down the barrel.
I like guns for the physics of the things.