When I went to Mull it was mid-late May and by then the breeding season was well and truly on and all the summer visitors were present.
I can't remember names of many of the places I visited on Mull itself since I was on a land safari tour on one day, but we saw Great Northern Diver, White-tailed Eagle, Short-eared Owl, Peregrine, Hen Harrier (how about that for a list of raptors all on one day?), Tree Pipit, Redshank, very, very good sightings of Otters on the coast.
Will you get a chance to go out on a boat trip? I'm not sure if you'll be a couple of weeks too early for the height of activity, and the weather might not be great, but going out to the Treshnish Isles on one day, and the next to the Cairns of Coll, including lots of time just in the middle of the sea scanning the surroundings turned up: Puffin, Manx Shearwater, Gannet, Razorbill, Guillemot, Pomarine Skua, Shag, Rock Pipit, Great Black-backed Gull, Herring Gull, Minke Whale, Common Dolphin, Harbour Porpoise, Common Seal, Grey Seal amongst many others.
I loved it, and I can't recommend a boat trip highly enough if you get decent weather. The experiences with the sea mammals was amazing. Going full speed and having the dolphins riding the bow waves, oh, it was absolutely exhilarating, then switching the engine off and drifting in perfectly calm seas while the porpoises by the hundred, and the whales came close - just hearing them breathe is something that will stay with me forever.
The Treshnish Isles were busy with lots of other groups, but you seem to have much more space to yourself that it doesn't feel as crowded as say the Farne Islands, and the Cairns of Coll, being uninhabited gems in the sea were just perfect places to stop and chill out for a couple of hours.