Since he was already married according to the 1940 census to Evelyn R. I doubt if the 1947 record is his.
Unfortunately one must have the mo/day/yr to obtain a copy of an MD marriage license for the period during which he was married.
You could try to obtain a PA birth certificate but without a place of birth or parents' names a match may not be possible since there may be a number of Harry E. Byrne's born on 08.25.1910 or his name may have been spelled differently or his birth not registered. PA births are restricted for 110 years so the online index for 1910 is three years away. As a great grandchild you may request a regular certificate. It might be worth the $10, an SASE, and copy of your ID. Here is the link, if interested:http://www.portal.health.state.pa.us/portal/server.pt/commun...
You will have to show unknown for parents' names and place of birth.
Another source would be his application for an SSN. My understanding is since he was born more than 100 years ago, SSA will release parents names assuming he entered the information.https://secure.ssa.gov/apps9/eFOIA-FEWeb/internet/main.jsp
(If you don't have it, his SSN information is on Familysearch.org.)
I noticed on the 1940 census he listed his occupation as a mechanic in a steel mill (perhaps Sparrow's Point). Do you know whether he retired from the steel mill? If so, he may have been a member of the USW, and there may be a union record available that might show place of birth. He may have had to submit a birth record to obtain benefits. I believe the USW office is in Pittsburgh, PA.
I think that exhausts by thoughts on what might be available.