i think you are overcomplicating things.
The MT 103 advice is simply a tranasfer receipt they can refer to while they wit for the money to land.
Using Wise, there will be no wait (at least mot of time, depending on the total.
As others have suggested you can also transfer to your local account and then make an immediate transfer to the hospital that way.
if, though i highly doubt this is the case, the transfer must be a swift transfer, with most currnecues you have that option as well using wise. it just adds extra fees and delays into the mix,