Percy, how do you intend to make the chamber spherical?
Hydrazine and HAN are both liquids. The propellants would need to be injected in a manner similar to a car engine cylinder, but chamber geometry from there is up to your imagination since it can essentially be a closed tube, excepting the action to bring the bullets in, the propellant injection system the ignition mechanism, and the muzzle.
You would need a reasonably clever system to ensure good sealing, as the propellant gases would be rather hotter and of smaller molecular weight (which is half the point of the exercise) than usual. The advantages are enormous, however.
The propellant could be stored in a tank of any geometry. Bullets, rather than cartridges would be stored in the magazine meaning a much higher density of rounds for a given length magazine. The advantages are similar to those of caseless ammunition, except without the bothers of ammunition integrity, and offering potentially higher propellant energy densities.
I would load the bullets into a mechanism similar to an aircraft revolver cannon, and slide the revolving cylinder backwards to seal it up against the chamber; perhaps with a system similar to that in the Nagant revolver. To fire, squeeze the trigger, which releases a sear connected to a spring-loaded syringe-pump which takes a consistent amount of propellant into the chamber. A catalyst in the chamber could cause the propellant to detonate or, if this is deemed insufficiently safe, ignition could proceed by electric spark.
Hydrazine is used to keep com satellites on station, start the engines in F-16s and powered the ME-163. It's not a widely used technology, but it's consistent enough to be used IN SPACE after years and years of bombardment by solar radiation, micrometeors and who knows what else. It's nasty, nasty stuff, but it works every time.
Alternatively, HAN propellants could be used. There is less industry experience with those, but they're generally more benign, slightly more powerful, and I think, no less reliable.