If you want one dated 75-80, then like you, I reckon it's a Hamilton or CWC W10 Mechanical General Service Watch.

https://cwcaddict.com/general-service-mech

Maybe start with a WTB here or on MWR.

Smiths (and probably 1945 WWWs) would still have been around although not marked in your date range.

I did have a Hamilton W10 ten years or so ago. Sold it for around £175, so just a picture of my Smiths.