And then in a few thousand years we will be kicking ourselves for incinerating incredibly valuable resources.
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.
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.
My point is that you can't cancel out the velocity of your orbit around the sun using solar sails.
It's all a moot point anyway since solar sails are so ridiculously impractical that this would basically never work in real life regardless.