One way to get rid of the radioactive waste from military drives is to dump it into space right out of your cargo bay. If you are in a system where a strong police force is watching, this can get you in trouble even if you dump directly after your jump into the system. In such systems you should simply sell your waste or (if radioactives are illegal) find a reliable merchant on the black market who takes it back.
You can have loads of fun if you try a few highly illegal dumping places. A space port is a very nice place to dump your waste on. Some people prefer to dump their radioactives into the still open landing bay of an underground spaceport. You can even fling your waste into a long range cruiser that waits outside of some space stations. Of course you can do the same with mines for the thrill of finally seeing a mine hit something!
There seem to exist systems where you can get real money for your radioactives. Look out for systems in the state of civil war. Sometimes you can sell your radioactives there on the black market.