A handout available at the USS Cairo museum at the Vicksburg National Military Park has crew muster roll of this ship.
Four sailors are listed as having "black" skin:
George Antone, E. Freeman [there's an interesting last name], J. Mitchell, and William Robinson.
Handout also lists date and place enlisted, term of enlistment, rating, where born,citizen of (state or foreign country), age, occupation at time of enlistment, height, and eye, hair and skin color.

I'm sure this handout is available by mail from museum/national park, or contact me and I'll make a copy and send it to you.

Interesting: both Antione and Freeman enlisted in New Bedford (shades of Moby Dick) and both listed "sailor" as their occupation. Mitchell listed no previous occupation (prehaps the recruiter did not press, although Mitchell was no youngster and his age is listed as 29). Robinson was a "boatsman" in civilian life.

Also, several more sailors are listed as having "dark" skin, but anything further on their race is speculation.

I always look for the humor in primary sources. One sailor, J. Murray is shown as having "florid" skin at time of enlistment. Wonder if he was sober when he joined up and muttered "what have I done" when he found himself oppoisite the Confederate shore batteries at Vicksburg.

Also, there were three fellows named Thomas Brown on board the Cairo This must have made the commissioned and petty officers nuts.
The one noted as "Brown, Thomas (3)" islisted as having "yellow" skin.
Maybe an immediate trip top the ship's doctor was in order here.
Browns 1 and 2 may have been related (brothers?) as both were born in Scotland. Brown number 3 was born in California