Looking for low-shrink solid hardwood advice

I am planning to build a pretty intricate wooden mechanism, not a clock but a combination lock for a chest. Of course I could use good quality plywood to avoid the inevitable shrink and expansion problem with humidity but for aesthetic reasons I would prefer nice solid hardwood.

Can somebody give my a recommendation for a wood species that has proven to be good for clocks that is low shrink, reasonably hard, not splintering, machinable and obtainable in a well sorted hardwood lumber store? The parts will be rather small so it is O.K. if not cheap. I guess Teak and Padauk might qualify but I am not sure what else may be better. FWIW the parts will not be glued so no problem if oily.

Thanks,

JB