The Insert has a size of 26,7 x 26,7 x 8,5 cm, so it may also fit in other wave core boxes, but you need to confirm the dimensions first.
The card boxes were designed to support sleeved carts, but I really doubt that you could fit all cards sleeved, I was planning to sleeve only the Nemesis cards, but I haven't tried yet.
The insert has plenty of space for tokens and extra spaces for dice, which I find more useful than most tokens that come with the game.