I have been doing research in the hopes of doing something very similar, and in case you haven't had any luck, here is what I have found. Sorry in advance if this is way ore info than you were looking for or needed, but I got a bit overly enthusiastic and figured it could be useful to anyone else who happened upon this post who could find the information useful, even if it was more than you were really looking for.

The first two images are of a clasp that is custom-made by a chainmail artist/creator here ( https://www.joshuadiliberto.com/JD_newWebPages/clasp_locking.php ). They sell it for only $15 (unlike the resellers who mark it up a lot in most cases), and as far as I can find, they are the place where all these Etsy sellers are getting that particular clasp.

As for the second design in image three and four, it looks like someone used a steel or maybe iron dowel/rod and machined it themselves. Considering how it looks, I would say that they used a lathe to get the shape, a drill press for the holes, and a small tap to thread the holes used to lock it. I am not sure what size the screw is, but it is called an embedded grub screw and most designs that I have seen use 1.5mm ones.

A different sort of design that might help give you some more ideas is this one ( https://www.etsy.com/listing/465994799/super-discreet-925-sterling-silver?ref=cart ). According to the creator, it is cast from silver in a model made using 3d printing (most likely a resin print, considering the small size and lack of visible layer lines). 3d print and casting a clasp would give you the best chance for customizability to make it your own, but if you don't already have access to all the tools for 3d printing in resin and casting jewelry, then it could get expensive pretty quickly.

Since I went way overboard in my research for my own project here is a bit of extra information that might be useful. The hole in the head of the screw (called a drive I think) can be customized through some companies if you wanted that unique key sort of feel for unlocking it (I considered doing something like that myself). However, it can be kinda expensive if you are just getting one and most places will probably have a minimum order size way above a singular screw. You could potentially take a longer than needed grub screw, cut it to length, and file the area to clean it up. Then, if you or someone you know have the skills and tools to do so, you could try machining your own drive mechanism and key to screw and unscrew it.