We'll have to pack it very carefully in any case. Perhaps we should assume that this will happen and work with that scenery in mind. The concept of a fire resistant box is not new at a smaller scale; We can vitrify the less dangerous waste and store the crystal in steel containers. Then we could theoretically design explosion-proof containers for it with some outer sacrificial disposable layers made of a plastic clay-like matherial or so.
Is much worse than that :-). The "space solution" can be split in three different possibilities. I will name the first "The slingshoot"
We have succesfully used a "Slingshoot" approach to put heavy things up to 100t in the space many times. Hubble telescope (12t) or the orbiter from the space shuttle (100t) fall in this category.
We could split our waste in chunks of 500Kg, pack it really well and just put it in an orbiter; the problem is that we can't go really far with this system (around 500 Km or so). We just will put the waste in a low orbit where things can fall again into the earth sonner or later. We had the Thiangong-1 case in 2018.
Thus this "solution" after a few years would be the same as dumping the waste into the sea, but in a very expensive and creative way.
