It all depends on which agent is checking you in. Some are stricter than others, but for sure, your carry on will be weighed. There is a bag sizing thingie at the check in on GC, which I have seen used.
An unsecured bag on the lap is a bad idea. If there is severe turbulence or a sudden stop on landing it becomes a missile that could hurt you or other passengers.
Some of NW Dive Dawg's suggestions are weasel like or frankly dishonest. The Airlines have rules for a reason.
The Saab and the Otter do not have overheads and the space under the seats is tight. Cayman Express will check your excess carry on, usually at no cost. My camera case is almost the same size as the OPs and I have never, ever been allowed to carry it on the Cayman Express planes. In all the many flights I've taken with them they have never lost or left behind my camera gear or carry on.
If the flight is overloaded, you might not get your suitcase/duffle until the next morning; so I always keep my reg, mask, bathing suit in the carry on. That way, I can still dive in the morning with rental BC, fins and wetsuit if I have to.