Not to spoil the adventure aspect of this, but have you looked for small timers on eBay, Google's photos, etc.?
Or the kitchen gadgets aisle at MartMart? I have a bunch of little $0.99 kitchen timers in my lab, LCD and buttons, guts are probably your postage stamp size, one watch battery.
Strip it and connectorize the LCD and pushbuttons as a "programming fob", lose the piezo element (its drive might run you a photoMOS?) and you've Muntzed it good.
Like a sculptor who "chisels away everything that's not art". Sorta.