....I have only one Hawes. Photos are included.
I had forgotten that the second one was traded off.
The second photo shows the SN and the first character is a "1".
The missing revolver was a Remington and it was marked in a way identical to the Navy shown in the photos.
I confess, I do not remember the serial number nor whether the first digit was an "H".
I do remember that there was no marking on the side of the frame that looked like your photo.
You can see from the photo above that the markings on the Navy are fairly nicely done.