That Mormon index site gives a Thomas Henry Wadsworth married Oct/Dec 1927 in Carlow District Ref vol 3 page 234
You can buy a copy from the Irish Government site, but cannot do it online, you have to download the form and send it with credit card details to Roscommon.
Carlow District does apparently cover parts of Laois. You would need to check what it does cover. As you do not know his wife's Surname, you cannot do the crosscheck to avoid haing to buy the cert.
There is a Patrick A Wadsworth born in Carlow District in Jul/Sep 1929 with mothers surname of Maher. When I plug that back into the Mormon site, it is indeed a Mary Maher that marries in Carlow then
That's the family group certainly, if your man is Patrick A Wadsworth then its him, if not then there do not seem to be any other options in Irish records.