The Manx Telephone directory is on line see http://www.manx-telecom.com/ - there are at least 200 Wattersons in the directory - ignore the one t or 2 t distinction, this is probably one of the more standardised names ! Manx spelling until universal schooling was always somewhat phonetic.
Though I suspect you have left it a bit late for a May visit you could try joining the IoM Fam History soc and placing a notice in the next mag.