Checked the book "Early Bermuda Records 1619-1826" compiled by A.C.Hollis Hallett, Juniperhill Press, Bermuda 1991 and found the following:
1. Page 96, Baptisms, Moore register: Surname: Smith Childs Name: William, Father Edward, Mother Deborah, baptised in Paget, Sept.(?) 1772. Note states "Month Lost". Time frame is right for this to possibly be your William.
2. Page 111, Groom Marriages, Moore Register lists the Groom as Edward Smith, and the bride as Deborah Slackman, married 19 January 1772.
Hope this helps. Be glad to check further if you have any further data - such as whom did William marry, etc.?