Not sure of the actual measurements!!
"The system consists of a push button swivel attached to the sling (approximate diameter 9.4 mm, a little under 3⁄8 inches) which is placed into a mounting socket on the firearm (approximate diameter 9.6 mm, a little over 3⁄8 inches)."
Is it in the socket or on the surface of the insert?
Maybe the proper sized drill bit , used with fingers only to clear hole....
emery paper on the tip of a dowel rod