Kevin,
Ordained Clergy officiated at baptisms, marriages and burials so I am not sure how the type of ceremony makes a difference. Also they often performed ceremonies in Parishes to which they were not attached.
I am sorry I cannot give you a copy of of the Rev. Bourke's signature in the Airmyn records because the images are copyright.
Maybe someone else with access to the Airmyn records for 1905 to 1907 could check the records and confirm that the signature is the same as the one on your marriage record and that the burial record of Dec 21 1907 at Airmyn is for Henry Martyn Bourke late Vicar of the parish.
You could also look at Family Search and see if there is any information there. Of course it will most likely be a transcript but there are some original records there. You might get lucky. When the libraries re-open you could also check Crockford's Clerical Directory for the relevant time period and possibly newspaper files as well for further information.
I don't usually bother with the name of the person performing the ceremony myself unless they are related to the family which, in one line of the families I am researching, happened quite often.
Venelow
Canada