Finding some nice places on the internet but many do not have a/c. i am trying to get an idea of how crucila it is.
We were there (Vernazza) several years ago on May 17/18 and AC was not necessary. It was fairly cool when we started our hike (needed light weight jackets) but warmed a bit during the day. No humidity at all and evenings were cool. Sea of Liguria was cold but a few people were swimming in Monterossa.
We were in CT during the last weeks of May(not sure which days, but we had 2 nights toward the end) and we had no A/C in our hotel. We opened the windows at night to flush the air and it was fine. During dinner at the Castelo in Vernazza(highly recommended), we sat on the balcony with a view of the sea and my photos show us wearing light jackets. You should be fine.
We were there in July & did not need A/C. The walls of our hotel were so thick that the room was cool all the time. We had shutters & no glass or screen in our window, & didn't have bugs!