If, however, this is contingent upon a space elevator, I wouldn't give it much thought at this time.
https://en.wikipedia.org/wiki/Radioisotope_thermoelectric_ge...
If a well designed, low yield nuclear reactor can't be launched then firing random waste into space will surely draw many more protestors.
Also I'm often surprised by the volume of waste we're talking about here. Under this umbrella you have not only fuel rods but also contaminated materials (eg, building materials, soil), and the launch costs per pound are very, very high.
I think I heard at one point someone was trying to work out if they could safely evaporate water (heat of vaporization of water being much lower than most isotopes?) and just store the residuals but even that got pushback. Hanford, if memory serves, has a rather substantial volume of liquid waste to deal with, and some of the containment vessels are past their expected lifespan.
From the numbers I can find, the delta-v to achieve escape velocity from the Earth is just over half the delta-v needed to crash into the Sun. To "get rid" of something you need a big rocket. To get rid of it forever, the rocket equation means you need a rocket many times bigger to go 90% faster.
https://en.wikipedia.org/wiki/List_of_artificial_objects_lea...