Lynn, 'Heave Ya Ho' sounds like it refers to the Mingulay Boat Song, which starts 'Heel ya ho, boys, let her go boys'. I have it down as 'Trad / Hugh S. Roberton'. I think Roberton, conductor of the Glasgow Orpheus Choir, translated it from the Gaelic.
The member of the Battlefield Band you're thinking of must be Davy Steele who died recently. He wrote quite a few good songs, but definitely not the above. But maybe I'm thinking of the wrong song, and he did write one called 'Heave Ya Ho'.
Can't help you with the second song, but I'm sure someone else will!