It is less delta-V to launch something out of the solar system than it is to drop it into the sun.
Assuming you're not worried about nuclear waste leaving our solar system and becoming a problem for others, it makes absolutely no sense to launch it into the sun.
That seems a bit optimistic of a problem to have. Space is incredibly huge. For someone to accidentaly bump into it would have odds so huge I don't even know how to aproximate it.
There's no such thing as 'nudging' it into the sun. If you don't push hard enough, it will enter an orbit that coincides with earth's. And to push it hard enough you basically have to get it going away from earth at the speed earth orbits around the sun, which is quite fast.
Anything less, and it will be in an orbit that floats close to the sun then floats back up towards earth, more or less forever.
Assuming you're not worried about nuclear waste leaving our solar system and becoming a problem for others, it makes absolutely no sense to launch it into the sun.