To be honest, you always need some fact that you can hold on to tight when trying to find someone...otherwise we have just best guesses.
From what we have so far that you have mentioned, there are only a few hard facts so far for James Mutch:
He was a railway porter at the time birth of child was registered in 1908. Is this correct?
From this birth reg (he must have been present at the Registrar in order for his details to be included on the birth certificate) he gave an address of 19 Canal Street. (This info did come from the 1908 birth cert?).
You mention family contact with him in the 1960s when he lived in a cottage on Inverurie Road, Bucksburn.
If he did change his occupation soon after the birth of the baby, the only possible source of verification will be working through the valuation & electoral rolls for Inverurie Road for that period of the 1960s. There is some chance that someone else might be included (such as a wife or child) that then lets you work back with confidence. Without this type of verification, not sure how you will be certain that you are on the right track with the right James Mutch...
This type of search (valuation and electoral rolls) need to be done in person. Not sure if this is possible for you to do? See for example
www.aberdeencity.gov.uk/education_learning/local_history/archives/loc_electoralrolls.aspMonica