Hi, I have got a couple of Llandudno brochures with hotels listed, one from the late 1930's or early 40's which has the Dunoons proprietors as Mr and Mrs J. Pugh Roberts, the later one from 1954 has the proprietor Mr Frederic Lees., hope this helps.
Looking at an earlier source, from 1929 The Llandudno directory, there is no listing for the Dunoon Hotel but lists a Mrs Pugh Roberts at number 24 &22 - Mill House. The hotel as it is now looks like two or more buildings merged. there was another property number 26, called Marshlands.