Hello MPM, welcome to the Forum.
In the 1929 Street Directory the listing for "Coolbawn" is number 31 St Mary's Road, Mrs E Roberts, Apartments.
The Shop you mention is listed in the Trade section under "Milliners" - J. Roberts Cheltenham House, Mostyn Street, 1 North Parade,
The alphabetical listing is Roberts, J. milliner, Cheltenham House Mostyn St. res Cheltenham House, 1 North parade, Promenade. Hope this helps! I can't find a listing for a Gwilym Roberts, but there are several G.Roberts listed at various addresses.
(My great uncle was a Gwilym Roberts - he lived in Caroline Road in later years, but as far as I know he had no connection with the above business,)