SET SCREW SPECS FOR MICROPHONES
I know to some harpmics seem to be held together by magic, prayer, and duct tape. Some, like the TURNER "Challenger" series, actually do rely on a snug 'PRESS FIT' -like the lids on Tupperware - to keep their grills in place. While there are many specialized nits and chiggers of hardware involved in the fit and finish of some mics (drift pins, threaded rings, etc.) the most common I've encountered are SET SCREWS of one sort or another.
In answer to a question pertaining to the types or sizes of SET SCREWS commonly found at the OUTPUT end of the majority of harpmics, the overwhelming majority you'll find will be this size: 6-32. If this seems like code, it IS! The 6 refers to the screw size / diameter and the 32 indicates the number of turns the threading takes per inch. Typically headless screws, you'll find them in 'slot' configuration, to be driven by a small flat-head screwdriver (such as a green or red Xlite brand) and "Allen" or "HEX" configuration, driven by an "Allen" or "HEX" wrench -or key. These, rather than having a slot in their top, will have a hexagonal socket in their top into which the driver key or wrench is inserted. Over the years, SHURE has utilized both styles.
Just looking over your old posts on any info on removing the TURNER "Challenger" series grills.