You have several options using Disney transportation. Given that you will be getting married in July on the surface of the sun, there is really only one practical option (short of hiring a car).
You could take the friendship boat from the boardwalk to DHS. From there, you would walk from the boat dock at DHS to the buses which would take you to the Grand Floridian. There are better bus options (see below).
You could take the boat to EPCOT, walk through EPCOT (everyone would need a ticket which I assume they would have anyway) to the monorail station. Take the monorail to TTC and then the resort monorail to GF. While this is your only non-bus option, in July, in wedding garb, this could be brutal. It is a good walk from the Int'l Gateway to the monorail station.
Your best best, to my thinking, is take the bus from Boardwalk to MK. Walk a relatively short distance to the Monorail station at MK and get on the resort monorail. That minimizes the walking and you won't need park admission.
I think you would be best to hire a car but if your budget doesn't permit, these are the options that occurred to me.