Poor Paddy On The Railway - The Dubliners, feat. Luke Kelly on lead (from 'A Drop Of The Hard Stuff', 1967)
https://www.youtube.com/watch?v=B5XTjA7ft9sEwan MacColl recorded an early version, and I actually didn't know that The Weavers had also done it, and Pete Seeger later on his own, but to my ears, The Pogues' version owes a huge debt to the Dubliner's arrangement and Luke's vocal. The Dubliners and especially Luke Kelly were a such a huge influence on Shane, and it's maybe heard nowhere more clearly than on The Pogues's recording of this song, so this is the one.
Waxie's Dargle - Sweeney's Men (released as a single, 1968)
https://www.youtube.com/watch?v=GKExPzTWFJURecordings go back to 1958 with Dominic Behan and Ewan MacColl on 'The Singing Streets', and of course The Dubliners did this one as well. I think we will find that Ewan & The Dubs have done most of these songs first! However, Terry Woods was in Sweeney's Men, and this was an early, groundbreaking electro-acoustic/folk-rock release, so this is the version i would pick.