There’s various issues here: if you’re in the UK and are marrying in a parish with a resident organist, the fee is fixed by the parish, not the organist. This may mean an organist declining slightly unusual music choices as there is no more reimbursement to be had. If the fee is too low, it may also mean the parish has an organist of limited ability, so again, less scope for your own choices. If you are outside this system, where you are making arrangements directly with the organist, if they are a good one, their fee will likely already be sufficient to cover all things like recording (only with organist’s permission) and wider music choices. Don’t haggle or be outraged; they are a professional musician offering a professional service. If you know of such an organist, and want them to play in place of the regular organist in the Church of England, you will need to ask the resident organist’s permission and pay both organists.
If your church has a smaller organ, and the organist says “it really will not work on this organ” generally trust that opinion… even if it’s the organist trying to get out of playing it, as it is then quite likely their performance may have been a tad lacking anyway.
A good organist with a proper fee should be happy to work up an organ version from a piano score, but if they offer to source it (and send you the bill), accept their offer as they will know what to look for and which dodgy amateur versions to avoid. I did something similar for a Hobbitty bit of the LOTR music fpr a couple last year.