While I haven't found anything on an Edmund Timothy Hehir, one of the postings below refers to a "Ned" Hehir who left Co. Clare with his brother for Australia in the mid-1870's. He was likely born before 1850, which would make him a bit old for a 1904+/- marriage, but....?
I'm not clear whether you're writing from Australia or elsewhere, but have you checked with the Australian government for (1) a death certificate which might provide details
on his birth date and parents or (2) immigration records.
Good luck, Bill