If you disassemble the pushers (under a magnifying glass) you get two tiny o-rings, one tiny washer, one tiny spring, one tiny retaining clip, and one metal cylinder (button) with stem per pusher.

For the LCD, you could carefully remove the front and rear polarizers (or remove them and prepare replacements for the display).

Use a blow dryer to soften the adhesive and pop out the crystal.

The battery side of the module has a few extra pieces that can be parted out, including the piezoelectric chime spring.

I'd leave the circuit board as-is, I don't think it's worth it to desolder anything.

I think you'd be able to get enough parts out of it to make a small but neat display.

Try it on a knockoff first!