Fitting cue badge disc.

[crazy 8]

Hoping one of the cuemakers or woodworkers can give me some advice. If I was going to refit the badge disc on my cue (fell out) what's the best method and glue to use?
The drill hole is a fair bit deeper than the width of the disc so i was thinking maybe milliput epoxy putty to fill the void and give me a bit more working time? Thanks in advance, crazy 8.

[Bilston Cues]

Milliput is what I use. No mess and easy to build it up if need be to get the badge flush