Sorry I still don't quite understand where the piece of wire is.
Either - has it fallen down one of the tiny holes which the CPU pins fit into in the CPU socket - ie from above.
Or - is a tiny bit of wire between the bottom of the CPU socket and the top of the motherboard and the wire's stuck underneath.
If it's the first one, you could try removing the sliding part of the socket, turning the board upside down and then use some sort of suction device like a solder sucker
and see if it can be sucked out of the hole.
Alternatively a small tube over the hole and sucking hard on it may work but be careful not to swallow the wire if it comes out!
If it's the second choice short of desoldering the CPU holder, I don't have any other idea. Note that the holder is soldered to the board with a ball grid array (BGA) like the graphics chip so this is not really possible without the right equipment.
Drilling a small hold from under the board is as I've said previously a bad idea since you won't know what tracks you're drilling through as you go through the board layers.