1966 Omega Ladies Cocktail watch - crown replacement

Good afternoon,

I'm hoping to get some help with a crown replacement for a 1966 (via serial lookup) Ladies cocktail watch. My mother pulled it out of her jewelry box and wanted to see if it still works. Luckily it runs and the case looks to be 14k so I figured I'd get it serviced. The caliber is 650 and case is EE5799 with 04215 below it. I'm having difficulty finding info on the case/crown as I think ladies watches weren't tracked as much. The watch is currently at the watchmaker, and at some point in the past, the crown was replaced with something generic. The watchmaker was able to measure the current one at 4mm, tap 10, and noted it's slightly big. I've reached out to "Watch Material" people who were thinking a 3.6mm dustproof crown would work. Just wondering if anyone has a good idea of a replacement or can confirm? https://www.watchmaterial.com/omega-watch-crown-gold-22004/?searchid=0&search_query=22004 This is the one currently being recommended.

Also on a side note, if anyone has any recommendations for a replacement band? I think eventually my mother will give it to one of my nieces and looking to see if there's something more different. I've seen some gold sort of rope bands and some others, but they're difficult to find.

Anyways, appreciate the help, thanks!

l&w watch cases were made in the USA and do not have omega case reference numbers, so you will not be able to find the exact parts, unless you happen to find old ads for this model.
I should have a smaller sized omega crown and a generic gold plated bracelet that should suit your watch, if you would like to dm me i can send some photos.

Watches like this used dust proof crowns. Has a metal ring with spring that pressed against the case to keep dust out.

Had a load of them years ago, but all sold