So the bottom line is - whatever suits you and whenever! Alaska is an extremely unpredictable place. There are no guarantees that you'll see a bear, whale, seal, on any given day whether it is May, July, or September.
While you think it might be warmer in June than May, it can be warm and dry in May and wet and cool in July.
It depends on the location too. The panhandle is a rainforest and has different weather and animal activity than does the Alaskan mainland.