I guess its difficult to say must unless there is a record of where it it was used.
It looks to be a WW2 era pocket watch that has been reissued prior to the standardisation of NSNs; so would it have had a radium /tritium dial when made and then had been redialed by the MOD?
The reason for removing the lume was to prevent spurious Geiger readings on nuclear subs, (0552=Navy) why would someone on covert ops take a big pocket watch with them?
1. its totally impractical
2. it would be in someones pocket / day sack so the lume would not be seen anyway
It is a handsome watch that looks to be in very good condition but I think the price is a bit toppy.