The song "Who's the fool now" is a later reading of the Scots phrase "Who's fou now" - 'fou' meaning drunk. The whole song is a nonsense song, with nonsense images arising from the drunkenness of Martin and his 'man' - his buddy. As the Irish might say when a mutual friend enters a pub, "Ah, here comes your man".

"Clouting off St. Peter's shoon" is a nonsense sentence, imagining the man in the moon knocking the shoes off St. Peter - and the shoes of the fisherman refers to one of the many symbols of St. Peter as the right hand man of Jesus and his earthly successor. Other symbols are the keys, etc. As other posters have rightly said, St. Peter's faith (and shoes!) were tested when he walked on the water.