Sinead -- welcome to Rootschat.
I think you will struggle to find the correct Michael Dale.
Older than your Nan could just mean 1 year older or 10 years older -- he may have had a middle initial.
He may not have been born in Manchester itself -- and Manchester consists of many areas as well.
There are electoral registers from 2002 on the Find My Past site -- but you will have no idea if he is still in Manchester.
Your Nan may have taken out an affiliation order against him to pay towards your Mum's upkeep - but whether those records will be available I'm not sure. Local newspapers may just have something if he was brought to court.
You could concentrate on researching your Nan's side of the family and draw up a family tree for her -- finding her mother and father, their parents and so on through birth, marriage and death records - census records etc.
There are free sites such as Family Search, Free BMD, Free Cen -- etc and Lancs OPC (Parish Registers) when you get back to July 1837 (when formal registration of births,marriages and deaths started). That site is for Lancashire only -- so if you discover that your Nan's maternal side came from another county - Lancs OPC won't work for you, but you will still have Family Search or Free Reg which you could try.
Alternatively you could fork out and join a subscription site such as Ancestry or Find My Past.
Maybe someone else can think of a solution to you finding Michael Dale -- but it seems like it would be a shot in the dark at this point.
Good Luck though in your quest.