Of course, I can't predict the future. So sure, if we in the future have some magical Star Trek technology that would make space travel entirely safe and ordinary, sure. Won't happen with anything like chemical fuels though, thanks to the tyranny of the rocket equation. And if we have such magical Star Trek technology, surely we'd also have the technology to transmute the waste into safer elements that don't present a long-term radiological hazard (that we in principle know how to do already today, it's just prohibitively expensive for little benefit)?

In the meantime, while waiting for the magical Star Trek future to arrive, I'd much prefer if we'd store the waste we have and continue to generate in a safe and responsible manner. Which, whether we do reprocessing or not, would involve deep geological disposal. If we later come up with a significantly better idea and for some reason have a motivation for doing something, sure, then we can dig it up again and shoot it into space, transmute it, or whatever the idea at that time is.

What I'm saying is that with anything like current day rocket technology, disposing of nuclear waste by shooting it into space is just a laughably insane idea.