I'm looking at Palma, Majorca as well at the moment. I've never been there, but am toying with a last minute transatlantic cruise from Barcelona to NY which starts with Marseille, Livorno, Civitavecchia, Majorca and Lisbon. A dream itinerary.
The cruise fare is just crazy cheap at around £40 a night solo, but it is NCL, and a ship 3x the size of any cruise ship I have ever been on. I also have something else on before that cruise, and am struggling to get to Barcelona in time- I am literally short of 12 hours.
So pondering.
Personally I would just do my own thing in Palma- maybe use the HoHo bus, walk the 45 minutes each way into town from the cruise terminal, or use Citybus #1 into the centre. Maybe do much of the above, and I want to do the Soller Tram (one way) returning to Palma on the good bus service, and maybe the main line railways toward the north end of the island.
It certainly isn't the sort of place where I would see the need to do an excursion, ship's or otherwise.
Be aware the Cathedral is closed on a Sunday, New Years Day, the Epiphany, 20 Jan, Maundy Thursday, Good Friday, Easter Monday, 10 May, the Assumption, All Saints Day, Constitution Day (6 Dec), the Immaculate Conception, Christmas Day and St Stephens Day.