Just bring them a paper 8710... You'll be in and out in 10 minutes. You don't need to in fill your flight times on the 8710 unless you REALLY want to. CFI cert or FOI results, AGI results, and a photo Id. They never asked to see my medical or my pilot cert.
While you're at the FSDO it never hurts to ask a few " hey, I want to be a more responsible aviator/CFI, what do you think I should do?" sort of questions. Any opportunity to make a good impression with the Feds could be worth its weight in gold should you run afoul of them later.