The US alone has performed 520+ atmospheric nuclear weapons tests. I'm not suggesting adding to that number, but perhaps there is a method to get nuclear waste off-planet.
The difference is large. If you blow up a nuke without contact to soil and stuff there is very little left for dangerous long term contamination. Hiroshima isn't dangerous to live in. Chernobyl is.
If a rocket blows up and spreads whatever is left when we removed it from a nuclear power plant that would be bad.