If you are flying in on a Saturday, I would not chance it with a group of 7. I just came through customs there about an hour ago (from the 3:30pm arrival on United) and we were through in about 15 minutes even with having to fill out the immigration forms in the hall because United didn’t provide them on the plane. But keep in mind that you have to go through immigration, pick up your bags, clear customs, recheck them with cayman airways, then go back through security. Late in the day on Saturday or just about any other day of the week, 1:45 is plenty of time as long as the arriving flight is on time. But midday on a Saturday, you are going to have more flights coming in and more going out, so both immigration and security will be slower.
My own feeling is that with a group of 7, I would take the later flight because you never know what may happen and the wait is less burdensome than what happens if you miss the flight and the later flights are full.