Crafting a digital watch
The quartz crystal should be the least of your problems. You can find them in miniature dimensions (2mm diameter x 6mm length) at any distributor. You may have some trouble to find the LCD, though. Microcontrollers in small packages are readily available, but they usually don't have enough I/O pins to control the LCD + some buttons. In common watches you'll see that they solved this by bonding the die (with sufficient I/Os) directly to the PCB. Standard components are never used for the battery holder and the push buttons, because they wouldn't fit. Instead, custom made metal metal strips are used.
Frankly I think this will be a difficult to do. If you really want to build a clock I'd suggest to make it a table top clock.  

The main difference between you and the watchmakers business is that you want to build 1 (one) watch, while they build them in large quantities, which allows them to use custom components at a low cost.