Do you recommend going on your own? Tours often offer special experiences that aren't possible on your own, but I don't know if that's the case here. Your suggestion is interesting...I’ve been to the GBR myself a couple of times and throughly recommend catching the ferry from Cairns to Green Island. Once you arrive on Green Island, you can snorkel off the reef by yourself and I saw green sea turtles, rays and a vast array of fish.
On the return ferry ride I saw a video promoting paid scuba diving excursions, but everything in the video I’d already seen by myself. The waters are teaming with life.