That was a short lived marriage - barely 3yrs.
His earlier marriage was even shorter - he married Ethel G Stradling in the June qtr 1935 and she died in the March qtr 1937 aged 42 then he married Beatrice approx 6mths later - all of which you already know.
The marriage to Beatrice must have broken down before 1940 so trying to find what happened to her between then and 1965 you are in a period when there are no records to show what people were doing at that time.
Her siblings will be long dead by now but may have left family in the area.
You could buy a copy of her death cert to see who reported her death but if it was one of her siblings that is not going to help you given it was 50yrs ago.
To look her up on electoral registers pre-1965 you would need to know her address and as she clearly did not re-marry that's another dead end
Shanagher is an unusual surname - particularly in Wales
To find her burial - you would need to establish exactly where she died (from her death cert) as here are all the areas covered by the Swansea RD
http://www.ukbmd.org.uk/genuki/reg/districts/swansea.htmlThere is no probate entry for her to help with an address
https://probatesearch.service.gov.uk/#wills