Your application package should cover more than your coursework experience and academic success, which is something an admissions committee can read right off of your transcript. They don't need an instructor to tell them you got an A.
Your promise as a researcher will be something an admissions committee will be very interested in. There may be other ways you can cover this elsewhere in your applications package, but I recommend that at least one of your recommenders be able to speak to this in a letter, whether it is one of your local profs or your REU mentor -- though if you has a positive interaction, I'd really encourage you to ask the REU mentor for the letter, unless your other potential letter writers are stellar. The REU program is quite a feather in your cap, and you should highlight it.
If you choose to go with your local profs, I would recommend not going with someone who's entire interaction with you was having you as a student in a course, unless there's something more than you just sitting in a room and getting an A on homeworks and exams -- again, your transcript will cover that. You should focus on profs you've interacted with extensively during a course -- especially for those courses you've done an extensive project in, and the prof watched your progress on the project. It makes for a more meaningful letter.
You didn't talk too much about why you don't want to ask the REU mentor, other than the limited 9-week interaction. A 9-week direct interaction is a LONG interaction, but if your mentor runs a large group, and you didn't work directly with them, it is possible the interaction was, indeed, limited. If this is what you're worried about, there may be a person in the formal mentor's lab that might be a more appropriate letter writer than the mentor themselves -- maybe a high level grad student or postdoc who you worked with directly.
If your concern is that you don't want to bother your mentor, just put that right in the trash!! Mentors in these programs have an expectation that they'll be solicited for letters. Also, one shouldn't develop a reticence to ask for support when you need support.