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There was a programme I saw on TV a long time ago (it could have been anywhere from 8 to 20 years ago). I think since that "episode" was self-contained that it was either an episode of a series similar to the Twilight Zone or the Outer Limit or it could have been a movie.

There was a disease (it might have been called Rigum) and those infected were exiled to this ship. The story I think starts in medias res, so the exiling had already happened and this disease was a fact of life for the inhabitants. The disease caused the human bodies to mutate. The captain had his hands extra large, and his lover had her chest entirely with this gooey transformation.

A military guy (he might have been wearing white) comes asking for a sample of their blood or DNA in exchange for a cure and a ticket back to Earth if they succeed. The disease had mutated so whatever countermeasures they had no longer work. He himself had the disease, and shows it to the Captain to try to earn his trust. The Captain refuses, and his crew mutinies against him and kills him. They agree to the Military guy's request.

When the Military guy comes back, he brings back more exiled people instead of a cure, so it looked like the cure didn't work. The current Mutineering Captain commits suicide, since he didn't listen to the previous Captain and had killed him. The previous Captain's lover then takes command of the ship.

I looked for a long time based on the disease name but I must have remembered the name wrong since I couldn't find it. The show was in colored. It was in English.

This might be an episode of "Masters of Science Fiction" (2007 TV series), called "The Discarded".

This series debuted on ABC and only ran for 6 episodes, each an hour long.

Here is a plot synopsis of this episode from IMDb.com:

After 37 years traveling in space in the hope of finding a new home, a
group of mutants face an interesting proposition. There are now only
93 discards left on the ship, less that one-third of the original
group. An envoy from Earth visits them to advise that the virus that
caused their mutations has spread but that they have managed to find a
cure. The only problem is that they need the mutants' blood in order
to manufacture the serum and in exchange, the discards are offered the
opportunity to return to Earth....but is the offer genuine?

—garykmcd

This episode was based on a short story written by Harlan Ellison in 1959 and was also known as "The Abnormals". It first appeared in an anthology called Paingod and Other Delusions in 1965.

Here is a clip from YouTube that shows the character with the large hand meeting the military type guy dressed in white: