2.5mm / (25.4 mm/inch) = 0.0984 inches.
It's gotta be 2.5mm. Music wire seems to run a bit big, sometimes, so if the wire is nominally 2.5mm it may actually be 0.099". Fortunately drills usually drill a bit bigger than their rated size, so a 2.5mm should work.
Can you open up the hole with a jeweler's rat-tail file?