A typical LED is approx 20mA, but since I don't know the exact model it is hard to be more specific.
But even if it is 30mA you will not exceed 1A with 16 of them (16*0,03=0,48), so in this application I would use a 1 or 2 A rated fuse.
The fuse is for shortcut protection, so it doesn't matter if it is a little higher.