It seems after reading this that the Records you want will not be found at the Southampton Archives! Sorry But you can always ask!
Cheers
Central index of Merchant Seamen
Crew agreements which record the contract of employment between the seaman and the employer were also established following the Act and do continue beyond 1857. Prior to 1835 crews are recorded in the muster rolls held at The National Archives.
Unfortunately from 1861, the surviving lists remain scattered amongst various repositories.
The National Archives
TNA holds a ten per cent random sample of agreements and crew lists from 1861 to 1938 and all the lists from 1939 to 1950. From 1951 to 1994, TNA only holds a ten per cent sample.
National Maritime Museum, Greenwich
The museum holds 90 per cent of lists covering 1861, 1862, and years ending in '5' from 1865 to 1975 (except 1945).
Maritime History Archive, Memorial University of Newfoundland
The Archive holds the remainder of crew lists (about 70 per cent of the total) covering 1863 to 1938 and 1951 to 1976.
All other lists up to 1989 have been destroyed with the Registry of Shipping and Seamen holding all agreements and crew lists from 1990 onwards.
So may be better to look possibly at other as above
National Maritime Museum, Greenwich
Maritime History Archive, Memorial University of Newfoundland (This I have personally found to be very good) I got all my Lists from there!
Good Luck
