+1 for replacing the socket wit a switched socket
your other alternative is to fill it.. but it will not look as good as covering it
As for the fuse, mine is running on a 10A fuse, but you can get a 13A version as well.
Mine has:
9 LED buttons, not sure how much ampage is coming off those...
2A TFT
2A audio amp
2A for the Raspberry Pi 2 (might be 2.5A)
0.5A LED strip for the marquee lighting
Note, these are 'max' ratings, they pull as much as they need, up to that amount
its a bartop arcade and so 10A is fine
depends what yours is though, i posted mine in case you also have a bartop