So Friday after rinsing watch, drying and connecting to computer I noticed a little yellow button on the desktop. It did look vaguely familar, so checked the watch, yep, minus the adjust button.
So now I have to decide what to do.
I think it's still water proof, the adjust function still works with a screwdriver or similar tool.
Here's what the watch looks like now.

I've pulled a button with actuator out of Pepe's case with the broken strap.
So here's the two of them. Mine's obviously broken because the cheap Chinese stainless has rusted through, Pepe's is in much better condition, he probably was more conscientious about rinsing after every session.

It wasn't a problem removing, but I'm not sure these old fingers can replace that tiny circlip.
Also I can't work out how the seal works, looks like a very neat fit for the shaft in the case, but a rusted shaft will quickly destroy and seal that relies on that. There's also no obvious reason why pressing the button should allow the unit to vent. That circlip is the only thing contacting the inner case when unpressed. The spring and washer are on the outside, so the washer only gets pressed harder against the case when button is pressed.
The circlip isn't going to create a seal against the inner case.
At the moment I'm inclined to leave well enough alone and see how long the other buttons last.
BUT it is a warning to be very thorough with your rinsing, you've got to get the salt water out behind the buttons