As you would like to get married on a quiet beach with little or no pomp and ceremony, it sounds like Jumba Ruins Beach in Mtwapa would be perfect for you. It is a quiet, almost private beach, you have the ruins as a backdrop and an ideal location for photographs and the wonderful Jumba Ruins Monsoons seafood restaurant right there for your wedding breakfast.
I have seen several big Swahili or Mhindi weddings at the ruins where catering has been set up in the ruins by the beach, but also some smaller scale weddings have booked Monsoons as the reception venue. Of course if it was low key, just yourselves and the witnesses an ordinary booking at Monsoons would suffice.
I would imagine that to book the actual wedding you would have to go through the Ruins Museum manager, who may be able to help with the wedding officiator.
and some photos of beach, ruins and restaurant