That will teach me!! Look here:www.northwalesbmd.org.uk
and then select the "Births" option. In the pro forma table enter your Dad's name but spell it "Willmer" [with 2 l's] for the year 1920.
There is a record that pops out - the local reference at Wrexham record office is WM/165/73 which may get you something from them. If you still live in the area you can go in and see them. No luck at Ancestry yet.