Ah, I see - the bat handle switch hole is so small 'cos only the metal pole goes through, so it just needs a bit of leeway, I suppose. They're still pretty large inside the housing, but that's of no real concern. I've been doing some Googling before starting the thread and I may be coming to the conclusion that what I really need to be searching for is "sub miniature"... who'd'a thought it? I can see some push button switches that seem to require a 6.2mm mounting hole, but they are momentary, just need to find the latching variant.
Volts and amps are pretty modest.... 5V and 1A, so I initially didn't think it worth mentioning, but I suppose some cannot handle that even.