Most reported injuries on river trips occur in camp or on hikes and are of the usual garden variety camping mishaps. Nights can be warm too. Spring and Fall are much cooler, but you can still expect temperatures in the 90's. Thunderstorms are possible anytime, but more likely in mid-summer, and the most rain falls in August. As soon as you are sure you are really committed to running the Colorado.
Outfitters fill some trips years in advance.
All require deposits to hold your space. On these web pages, I don't. What I do recommend is contacting every company on the Outfitters Page. If you do your homework, you'll not only find your outfitter, but you're likely to talk to some nice folks and learn a lot about commercial river running.