Update:
So I tried pliers and even though I placed a folded piece of cloth on the blade and was trying to be gentle some of the damaged part came right off, perhaps some air got in between the first and second plies but the rest is almost completely flat. Now that I see the previous pics a crack was already there so it was a matter of time I suppose.
Now, the top ply is missing and some of the second ply.
I assume now I can use sawdust or other wood waste and wood glue to patch it up?
Fill in those cracks, there is a risk that the glue will catch there and rip again.I just fixed my Petr Korbel after a hit on the table removed a big piece of the top ply. I removed the rubbers and kept the wood parts.
I glued them with wood glue. I used a clamp with two plastic pieces to press and hold it in place. After a few hours, light sanding and a light coat of varnish.
I'm happy with the result.