Princess ships do have wedding chapels etc and you can be married by the Ship Captain but I am not sure that this is legal for UK but only for US citizens but there must be a way around this. I know people do get married in some of the Caribbean Islands during a port stop and again this could be a risk is there was a problem and that port had to be missed.
My son got married in Cyprus and there were fairly rigid rules as this was a RC wedding and all the letters of freedom to marry had to be sent from the Parish he was living in. I think this letter had to come from the Bishop to the Priest who was in Paphos.
The responsibility for having all the correct documentation is on the persons being married and not the tour company. I went out a few months ahead and met with the Priest etc just to absolutely clarify things as well as check hotels etc etc. You would need to look at various companies and then make enquiries as to what is legal. It would be much easier if you were just having a civil wedding. It was compulsary that they had the civil wedding and whilst it could have been on the same day they had it 2 days ahead and this is their legal date of Marriage.
Good luck we all had a great time all 31 of our family and friends and then a big do in Ireland for 150 guests later.
Look at some of the boards concerned with weddings and this would also be helpful. Talk to a good travel agent possibly who deals with weddings abroad.
Sue