You don't need to know. The Medical Officer does need to know.
Actually, I think that there may be a good reason why this question comes up from time to time, and why people do have a need to know. People now join up as submariners (as opposed to being side-swiped at some point during or after Pt I), and are in the position where they may fail a test over which they have no control, and which could cause their hoped-for career to be terminated, as there is no guarantee that they would be offered a place as a skimmer (in fact, they are told that the chances of going skimmer after joining as a submariner would make JaydeMarie look like Pinkswordswallower's boy). It is not, therefore, unreasonable for them to enquire what extra things are included in this examination, as it could help those who know that they have just scraped through on one aspect or other decide if their goal is unachieveable before wasting their time and our money attempting to join as a submariner and failing at the first hurdle, rather than accepting that they wouldn't make the cut, and electing to become a skimmer from the outset.
In the days of pressurised SETT runs, lung function was tested, and radiography of the chest carried out. I can't recall anything else being done that wasn't on a standard PULLHEEMS. With the demise of the pressurised runs, the end of Rush Escape as a recognised and supported method of exiting a sub, and the insistance that pressurised tower runs would be carried out only as a last resort, I can't see a valid reason for even those tests to be done any more, other than someone not having the testicularity to make it so. So, if anyone on here does actually know what extra things are included on a submariner's medical, and more importantly, why, I for one would like to know.