this answer shows a period of time when the ISS lost only 10 meters of altitude per day, and this answer shows a period of time when it lost about 100 meters a day. Based on this kind of analysis that requires a delta-v of between 6 and 60 mm/sec. The ISS is about 400,000 kg.
update: this answer shows more extreme periods with altitude losses of between 7 and 400 meter per day! But let's use the factor of 10 range for our working space and assume that in an emergency rocket propulsion is still available.
So for the first range described the daily impulse would have to be between 2400 and 24,000 kg m/s (Newton-seconds) or about 120 to 1200 Estes "D engines" or about one "M" engine per day.
If you had for example 1 kg of waste to shoot per day, you'd have to shoot it at 2400 to 24,000 meters per second. That ranges from suborbital (it would hit the atmosphere hard in half an orbit) to escape from Earth's gravity even though it's retrograde (24,000 - 7800 - 11,200 = 5000)!
For comparison, Wikipedia's Muzzle velocity says:
Firearm muzzle velocities range from approximately 120 m/s (390 ft/s) to 370 m/s (1,200 ft/s) in black powder muskets, to more than 1,200 m/s (3,900 ft/s) in modern rifles with high-velocity cartridges such as the .220 Swift and .204 Ruger, all the way to 1,700 m/s (5,600 ft/s) for tank guns firing kinetic energy penetrator ammunition. To simulate orbital debris impacts on spacecraft, NASA launches projectiles through light-gas guns at speeds up to 8,500 m/s (28,000 ft/s).
So you will need a pretty substantial cannon to do this, and videos of "tank guns firing kinetic energy penetrator ammunition" will probably show some "kick" or recoil.
The ISS' structure is minimal; it is no heavier than is absolutely necessary to hold itself together, keep the air pressure inside and astronauts alive, and hold up when the Space Shuttle grabs ahold of it gently or a capsule docks.
It's not built to withstand such kicks.
So you'd have to shoot 10 or 100 smaller masses per day.
Good luck with advertising the ISS as a viable research platform for microgravity experiments!
The alternative would be to shoot 10 or more kg of waste per day at lower velocity, but you may run out of waste unless you break that pallet of old nickel batteries up into pieces and shoot a little bits of it at a time.