Have been thinking about getting an altimeter watch, but wondered how I would cope with little buttons while wearing gloves. This is one solution I think it would be easy to knock up. I would probably do it in brass, for ease of construction, but if your brazing isn't up to it, quite honestly it could be done in wood - simply drill the sleeves in a block of wood and insert loose dowels. The only real weak point would be relying on the watch button springs to pop the buttons back out, though it would be possible to put springs in the sleeves, I suppose.
Of course I don't intend to wear the watch. The idea is that it would be strapped to the base bar.
(apologies for the crude artwork, knocked up on Paint)