Hi
@GR8FUL
You can be AOW/nitrox with 9 training dives
I've never been asked to provide a log to document number of dives, this includes liveaboards in the Red Sea, Cocos, Galapagos, and Revillagigedos. Many liveaboards have a easier/check out dive at the beginning of the trip. I've never thought I was even casually, being watched. I think the main reason for this dive is as a weight check, sometimes divers are using exposure protection or other gear they are not very familiar with. I suppose that if someone had a lot of trouble on this dive, it would be noted.
I agree with other comments. I would simply be very straight with the operator. I, GR8FUL, have been diving for 25 years, I have 200-499 dives (per your profile, I have about X dives in the last year and my last dives were on these dates. In addition, I am AOW. There certainly would be no harm in doing the checkout dive with the rest of the group.
I did not log my dives for the 1st 10 years I dived, it was not so common back then. I have logged all of my dives since 1997. I have them all in paper log and have the last 9 years downloaded from my computer. It would not hurt you to start keeping a log now to deal with situations as you have described. I would start a new log at your best estimate for your number of dives, and go from their. You can also download them from your computer, when you obtain it.
Best of luck in your diving. Where are you in Florida? I do quite a bit of my diving in Boynton Beach, Jupiter, and West Palm