Hi,
Without seeing the game and more specifically the code,project and menu I can't really propose to you how long it will take to complete, but this is the sort of thing I have done for my own games many times.
I'm guessing you want things like ammo/lives etc to be updated. The integration of the menu should be pretty quick (sub 1 day). As for stats and information updating it's difficult to put a timeline on it without looking at the project in more detail. Sorry to be vague.
Is the fps game using an asset from the asset store like UFPS? MFPS?
Anyway, hope to chat with you over the project and maybe we can work together on it.
All the best
Chris