Another way to approach this is by making a tree on ancestry, putting in the name of your mum's 'real dad'.
I'm presuming that he is going to be around the same age as (or a bit older than) your grandmother, so it may be possible to find a record for someone of that name and age.
Putting his name on the tree, you may get hints - which do need to be checked (not just accepted).
Also if you attach your mum's dna to this tree, then thrulines will work and hopefully be able to suggest some matches which are on your mom's paternal side.
hth,
Lisa