If you use a PA/sound system with handheld microphones, then cleaning the microphone(s) occasionally is an excellent idea.
As well as the hygiene benefits, spending a few moments working on each microphone also lets you notice any loose connectors or worn cables, or similar issues, so they can be pro-actively fixed before they cause problems during a service.
Microphone manufacturers Shure have made a video showing exactly how to do this with their equipment. And the procedure is similar for other models, too.
Note: the video refers to using Q-tips. This is an American brand of pressed cotton-buds.
If you have a lot of equipment, it may be wise to set up a regular preventative maintenance schedule and do a few items every week rather than trying to do everything at once.