I really think it's a bad idea to do this to instructors, but it is not allowed to use a CAP aircraft for commercial purposes, including flight instruction. The ONLY exception is for a DPE giving a practical test.
Honestly, I'd like to pay instructors for time not required by CAP. It would help alleviate the constant instructor shortages, and it seems only fair.
I can't speak for the Air Force paperwork, but honestly, the load isn't that bad. It's more than a flying club, but not a lot more. Yes, I have to do a Form 71 inspection every once in a while, but that takes like 5 minutes and it's a subset of preflight. There is some dispatch-like "paperwork" to be done before and after a flight, but it's a website (WMIRS). Basically, you have to say who and what's on the airplane, where you're going, what your schedule is, do a weight and balance, and a risk assessment. Afterward, you have to record your hobbs and tach, plus fuel/oil and results if it's reimbursed (otherwise no one cares). It's not THAT different from what I do on a family flight -- someone on the ground always gets informed about schedule; if it isn't a release officer or air ops branch director, it's a family member.
WMIRS seems modeled after a part 135 operation, but CAP is very careful not to call it "dispatch," presumably for liability reasons. Flight release is an authorization to use the aircraft, not a safety function (though they will call AFRCC if you're overdue by more than two hours).
There must be some paperwork for a mission. There just has to be a way to communicate your results up the chain so the planning section can do their thing. Otherwise, your effort will get wasted as it gets duplicated over and over.