All I have on the Gooding LP is the date, 1956, EKL-107 and the track title, "Waly, Waly." I don't know if this is the Water is Wide version.
I can't find Water is Wide or Waly, Waly listed on early Pete Seeger recordings. Only the late one, "Pete," 1982. Is there one??

Error on my part; never trust my memory- The verse "When cockle-shells turn into siller Bells" is in "Waly, Waly," Thomson, 1733, in Bronson's The Singing Tradition, Jamie Douglas, 4th verse of ten ("first printed in Orpheus Caledonius, 1725"). Thus not Irish. And no Water is Wide.
This may be already posted in the threads, but here is the first verse from Thomson.
O Waly, Waly, up yon bank,
And Waly, Waly, down yon Brea;
And Waly by yon River's side,
Where my Love and I was won't to gae.