If everything goes perfect you can make that connection but I would not try it myself. Pretty much anything that would delay you getting into Grand Cayman would cause you to get screwed.
Also, if you are booked on the 1:45 Cayman Air flight and you miss it, there is a chance you won't get on the afternoon flight as they are typically sold out unless it's midweek which in your case it is so you at least have that going for you. But if you miss the 1:45 flight, can't get on an afternoon flight, and bam....you spend the night in GC. I'd much rather book the later flight and hope to get on the early flight than book the early flight and possibly make neither.
Finally, even if you book all the way through with Delta, I don't think Delta will be responsible if you miss the connecting flight if it's because it takes too long to make it through immigration and customs. Not their problem.
I have done this trip many times and always book the later flight. From time to time I have been able to grab an early flight and I consider that a win but if not so be it. Honestly, four hours at the GC airport is not that big of a deal.