Regarding the cost of testing, our insurance covered a lot of it for our daughter. Her school suggested we have it done at a local Children's hospital in their kids psych area, and they did a complete testing working, including IQ and ADHD testing, and some other stuff I can't remember now because it has been several years. Of course, not every insurance plan would cover this, but it is worth checking. You might need a referral from your pediatrician, too, even if it is covered.
Regarding the reluctance to test, remember that you can just go for testing. There does not need to be any active "psychology" type work done with your kid (of course they need to work with them to test them, but they really don't make any effort to change/modify their behavior in this process). My kid didn't seem to mind it at all, it was sort of like games and puzzles to her. And... you do not need to share test results with your child or anyone else if you don't want to.
From my experience, the test results are quite useful. We just figured out (and by just, I mean YESTERDAY) that something the WISC IQ results show (a gap between verbal and nonverbal scores) explains a lot about some organizational issues D has, and guided us to an online group that may be able to help with some tips and support to overcome those. Without the test results, we never would have figured this out on our own.
Good luck!