Bit late to the party Babs, but when you buy buttons/screws together, they can be consider a match. The supplier usually knows what he is doing, and its worth thinking about 'collateral' damage that may occur should your shorter screws pull out !
That 'small' pilot hole you mention should not be too small. Even with soap/tallow on the screw, it does not take too much to shear the screw shank, this you do not want to have to deal with !
A minor point. Bearing in mind that your instrument likely has a polished finish it is useful. once you have decided where the screwhole is to be located, to make a small indentation at that point (I use a centre punch, but a suitable sized nail or the actual screw would do) just to ensure that your drill does'nt skid all over the place.
good luck
JohnH

thanks!