Just to clear up something that may cause some confusion, the "undercut head" is not the head diameter that is smaller. The term "undercut" pertains to the part under the head near the threads. The bottom part of the head is shorter so that the screw can have more threads. This is typically done for small length flat head machine screws because the length of a flat head machine screw is from tip to tail so to speak where as a button head screw length is only the threaded portion.
For example this link shows a #8-32x3/8" Non-undercut screw:
http://www.mcmaster.com/#cadinlnord/96640a123/=n6h4ng
This link shows a #8-32x1/4" undercut screw:
http://www.mcmaster.com/#cadinlnord/96640a122/=n6h5pl
You can see that the head diameter is still 0.312", but it is only 0.070" thick rather than 0.100" like the standard screw.
I just wanted to make sure that it is clear that if the snap ID is too small for the OD of the screw head, an undercut head won't help. If the screw head isn't seating down deep enough into the socket, then the undercut head may be your solution