I can respond only as a Captain, Royal Artillery, Retired, becoming "retired" more decades ago than I care to remember, after an undistinguished career.
In later life, I ran a sea-oriented business in Dartmouth, where the Harbour Authority recruited entirely from retired Naval people.
Business was still done, at that time, by writing letters, and I found that converting RA after Captain into a squiggle that looked like RN got excellent results from the said Authority.
However, I have also found that using any of the myriad possibilities offered by British Airways for a passenger's title, such as Lord, Captain, Prof., Sir, etc etc,, I've tried them all, has no effect whatsoever.
You've earned your title of Captain, which is more than I did, and you should use it in aviation circles on duty.