What can I use extra Project Cores for?
From the official FAQ
All PROJECT content will stay in your Hextech Crafting inventory once the event is over. If you prefer a tidy inventory, you'll be able to disenchant all PROJECT materials into a little bit of essence.
However I haven't found out how to disenchant anything in the client yet. I have a couple cores and some cache fragments myself and don't see a disenchant option.
EDIT:
The current plan per our project disruption guide is to make leftover items disenchantable. It doesn't seem to be enabled just yet! I don't have an eta on when that will be, but hang tight!
EDIT 2: It is now enabled, you can disenchant leftover PROJECT items for 2 orange essence each.