Some of the Gibson 345 have stereo Varitone, the Big D Varitone is mono but it sounds great. Evene more importantly wold be to use some of the best 10% CTS500K pots. They will add clarity and have a smooth custom taper. I also build my 335/345 rigs with 50's wiring, not the stock muddy modern wiring. Here is a pic of a "Lucile" rig I built a month or so back and shipped it to the EU.

Can a Big D Varitone switch replace the Gibson stock Varitone switch?
If so, does it sound better and be more functional?

I have two Gibson B.B. King “Lucille” guitars.
One that B.B.King signed and one that I have modified and I play all the time.

Wow, beware you are asking a carpenter/musician about computer stuff..lol
Looks like Zoso already has you covered