We did the trip from Little Cayman last year on a Sunday and the lines in GCM were long. We collected our bags fairly quickly after we arrived on GC and then we went outside and back inside to recheck our bags and go through security, immigration, and customs. I think 2 hours should be fine.
The only time we took Delta, they didn't open their ticket counter and baggage check-in until about 2 hours before the flight, so there wasn't any advantage to getting there earlier. We had to pile our stuff on a cart and take the elevator to the second floor and hang out at the Hungry Horse until they finally opened up for business.
Are you staying at Little Cayman Beach Resort? The reason I ask is that last year we had the option to pack a bag or two the day before we left. They put these bags on an earlier flight and they were waiting for us when we arrived at GCM. It was a bit of a rush to get our gear semi dried out and packed on time, but it was nice not to have to deal with them on our travel day until we arrived on GC.
One thing I didn't like about our trip home from LC. We waited at the tiny LC airport and then boarded the twin Otter which hopped over to CB. We had to deplane, collect our bags, go through security and then board a Saab Turboprop for the hop to GC. When we arrived at GCM we had to collect our bags and do it all again while fighting our way through the crowded lines to get to the departure lounge.
Of course when we arrived in Miami, we had to collect our bags and go through US customs and immigration before boarding the last plane for Chicago.
We visited 5 airports, took 4 planes, and traveled 12 hours just for a 1600 mile trip. Cayman Air offers direct flights from ORD during the High and Mid seasons but we were traveling in the low season and we didn't have a direct flight option from GCM.
Where are you coming from? If you can get a direct flight it will be worth it! And Cayman Air offers 2 free checked bags per person so even if the price is higher it may still be a bargain.