The size of the hole that the switch is going into looks about the same as industrial switches used on machinery. I used to design a bunch of industrial machinery, not the electrical part but I did do the drawings for the enclosures sometimes for the electrical guys. Eaton is one brand that comes to mind they have momentary push button switches. Siemens makes very nice switches as well.
And if you're not familiar with the industrial parts supplier McMaster-Carr, it is probably the best organized and best run website in the world for selling industrial components, tools and raw materials. And they have the best customer service I've ever encountered. If you call them you will instantly get a person never an answering system. There are less expensive places to get the same things at times, but oftentimes the hassle of getting the right thing from those other places or the customer service you encounter makes it worth using McMaster-Carr. Also depending upon how far you are from their nearest warehouse which they have many, if you order by 10:00 a.m. you can get parts delivered by the same afternoon! Also if you buy hand tools sockets and wrenches and screwdrivers and such from them usually it's from Proto brand made in USA!
McMaster-Carr Page:
https://www.mcmaster.com/momentary-push-button-pilot-switches