Well the Collard Hill version can not be the tune from "1883 Naval Songs, Wm A, Pond and Co", as he wasn't alive then ... :-)
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The song appears in
Book of Navy Songs
# Paperback: 160 pages
# Publisher: US Naval Institute Press (June 1983)
# Language: English
# ISBN-10: 0870211064
# ISBN-13: 978-0870211065

Don't have a copy, so don't know if tunes are therein ... might be an early used tune...

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Also appears prior in
Francis T. Palgrave, ed. (1824–1897). The Golden Treasury. 1875.
a poem written by
A. Cunningham

AUTHOR:        Palgrave, Francis T., ed., 1824–1897.
TITLE:        The golden treasury of the best songs and lyrical poems in the English language, selected and arranged with notes by Francis Turner Palgrave.
PUBLISHED:        London: Macmillan, 1875.
PHYSICAL DETAILS:        332 p.; 17 cm.
ISBN:        1-58734-038-0.
CITATION:        Palgrave, Francis T. The Golden Treasury. London: Macmillan, 1875; Bartleby.com, 1999. www.bartleby.com/106/. [Date of Printout].
ON-LINE ED.:        Published January 1999 by Bartleby.com; © Copyright Bartleby.com, Inc. (Terms of Use).

so a poem with no original tune ...

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another tune by David Parsons ..

so the claim (http://www.parsonsfamily.co.uk/music.php)

"A wet Sheet and a Flowing Sea, a song written by DP while still a schoolboy. (video on YouTube 2 mins 08 sec) " http://www.youtube.com/watch?v=tMOPmqlI4yo

maybe he composed this tune he plays (a rather dull staid and boring one compared to the tune my friend has!), but he did not write the words!!! (even as a schoolboy!)

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"A Good Sword and a Trusty Hand" also sounds insufficiently lyrical .... :-)