Meltslash has never been declared capable of destroying the core, we know that the core is protected by the information particle, but we don't know if meltslash is able to reach the core, and as I said, Raphael says he can come back with >infinite regeneration<, the skills or their data are recorded in the core, so Rimuru could still regenerate, if it is stated that for some random reason that infinite regeneration works differently with Rimuru would be one thing, but that's not the case, at least not yet
Even though meltslash can erase information, I think HGR only applies if you have even the fundamental aspect of your existence COMPLETELY erased, in this case it should include the core as well, since it is something that is part of Rimuru's existence and the core is essential for the existence of a being in Tensura, which Rimuru is not and has not been said to be able to do, but if I'm wrong and the simple fact of being able to regenerate the fundamental aspect of your existence (without being completely) is enough, then that's ok, it's still HGR