I get it, sea water isn't everyone's bag. Swimming isn't everyones potatoes and submersing yourself in the sex juices of a billion microorganisms doesn't raise everyones mast. Don't worry, the multitude of tour operators in Cairns will bend over backwards to fellate the guy behind them if it gets you on their boat. You can still see the GBR while maintaining a crisp do, people do it all the time, here's the tips.
Semi-submersibles and glass bottom boats are available in some form on most reef trips. Reef Magic, Down Under Dive and The Green Island Big Cat all have a variation of a boat with a clear bottom. Most of them are equipped with a marine biologist with a spunky attitude and a sharp wit, ready to tell you about all the fish and coral species you'll see. A glass bottom boat is exactly what it sounds like, where you're looking down at the water below. The Semi-Subs have a below-dech area where the windows are on each side as opposed to beneath you. These are good options for getting a clear view of the reef without donning a wetsuit.
Nautilus Aviation and GBR Helicopters do heli trips between the reef pontoons and the mainland - leaving from right at the Pier terminal in the center of Cairns no less. These trips are really exhilarating albeit a bit pricey and short lived - usually going for between $300 to like, as expensive as you want, and lasting from about 15 minutes to all day if you've got the pay. Helicopters are super fun no matter where you're flying and doing it over the great barrier reef is top notch - it's a whole different story from the air.
You can skip the outer reef altogether and go island hopping instead, The Fitzroy Island ferry goes most days and Fitzroy Island is low key the best place to see sea turtles in all of Cairns, being a sheltered island reef and not too far from the coast. You'll spot them poking their heads out of the water grabbing a breath it's really cute. Green Island is the other pick with multiple boats going every day, prime beaches all around, a crocodile zoo in the center of the island and a resort that I wouldn't recommend to anyone.
You've also got a litany of aquariums and zoos that get you right up close to the main event without a splash - the Cairns Aquarium is right in town, the Casino has a rooftop Zoo which is a hidden gem and if you're happy to grab a bus you can go out to Hartleys or up the hill to Rainforestation (although those last two are less reefy, they're equally beefy).
So don't lose your wig, there's plenty to do without dunking your head in the water, and even as an avid snorkeler myself, sometimes I just don't want to get wet so it's nice to know there are other options for the less aquatic ones among us.