Help with ID of 1930s (?) Naiad-like (?) Ref 125 (?)

When I purchased this watch off eBay 8+ years ago, I had collected information that I now cannot locate.

And after an afternoon of google-ing, I thought I'd finally burden OF with a request for help in ID and other observations; thank you, in advance.

Reference:
Both the interior case back and lug markings recount "125" (which is terrible google-fodder, given the cal.1041 125th ann. reference). In my limited knowledge, I'd expect this reference to be a 4-digit "CK" type reference, but no luck with an online-match, for exactness.

I don't remember the specifications for a "Naiad Medicus," but suspect this is a "Naiad" case.

Further, the exterior case-back recounts "9941432" while the movement bares "9050513." I don't remember if at this vintage this indicates a replaced movement/caseback, or if instead there was no such expectation at the time?

Caliber:

Given the above, I'd guess the caliber is the 23.4SC – the first movement produced by Omega with center sweep second hand. I see no movement inscription of this, which I seem to remember is not uncommon to the era.

Dial/Handset: I take the dial and "syringe" handset to be all original with very little deterioration.

Case: I'd take it to be ~30mm, crown excluded. I've never cleaned this case (or as mentioned, serviced the watch), but it appears ripe for a gentle cleaning to bring it into good condition (for a probably 90 year old watch).

Misc:

The band and buckle appear original to the watch.

Crown unknown to me if correct.

As for it's operation:

With the crown pulled full out to set time, occasionally the second hand jumps several seconds forward or back depending on the direction of time-setting pressure applied.

I've gently wound once and center sweep seconds tics along; I've let it wind down, though, since I've not serviced the watch and to avoid any damage to the movement.

In all: It's a beautiful little piece with seemingly all the bits and bobs.

Wonderful watch

9,05X,XXX would be more like 1939.

Thank you for your feedback and education.

Regarding the dial: it is still stumping me in my inexperience. I find many examples of this era with white/cream colored dials (unlike this black dial), all with minute numbering within the outer railway track (unlike this dial), together with much more tidy dial hour numbers (unlike this dial). Finding few black dialed comparisons, I’m only left to wonder whether the black dialed versions were possibly less tidy perhaps due to paint relief differences?

And then there’s your mention of “lume”; I’d assume these watches did not have lume? (Though, given your handle, perhaps there is a language nuance here?)

Still otherwise left assuming that this dial has been repainted. Feel a bit silly for having not picked up on that better before, though still blaming it on the lack of black dialed references 😁

Thank you both; I was certainly mistaken to say the band and buckle were “original to the watch.” On reflection, I suppose I only sensed they appeared to be Omega and old; I had no basis for placing them in the 1930s/40s 😵‍💫

Appreciate the correction