If you vitrified it first honestly it'd probably be totally fine. An arguably better plan is just get serious about reprocessing and work towards cleaner processes than PUREX. Not even necessarily a completely new process, just better controls around handling waste and making sure there's no massive liquid tanks just waiting to leak into the ground like the Hanford site. Most spent fuel is depleted uranium and not exceptionally dangerous to be around. If you can separate out the fission products and transuranics then you could drastically reduce the amount of waste needed to be stored, store it for less time, and potentially recycle some and get some actual use out of what is currently considered waste.

Just dumping fuel pellets into the deep ocean would be a pretty terrible idea though. All the fission products and impurities that build up as the fuel is burned lead to the pellets starting to crack apart. Any cesium or iodine would leach into the water quickly, it would not be a good day for Shamu.