Yes Alice thats correct so far as I know. The verse in the middle is:
"The first land we sighted is call-ed The Dodman,
Next Rame Head off Plymouth, off Portsmouth, the Wight,
We sail-ed past Beachy, past Fairligh' an' Dover,
And then bore away for the South Foreland light."
Sorry about the hyphenated words, I don't know how to do accents in HTML fonts, and if you don't use the archaic pronunciation it mucks up the meter.
Shank painter and cat stopper refer to ropes holding the anchor to the cathead, clewgarnets haul the corners of the sail up to the yard. Actually you would have to free the sheets and tacks before clewing up, but we'll put that down to poetic licence. :-)
Another snippet of information is that this is one of the few songs recorded as being sung on RN vessels rather tham merchant navy. I think Tawney also mentions this in "Grey funnel lines".