First, who ever told you anything about cat boats doesn't know jack about them. They're very shallow draft boats with the centerboard up. As an example, the Beetle Cat, although a bit small for what you want, has a board up draft of EIGHT INCHES.
What you might want to look for is something like a Com-pac Sun Cat
. The boat has a 14" draft board up... However, someone of your height is going to be at risk of getting whacked by the boom and certainly can't stand up in its cabin.
My boat, although probably out of your budget, would probably work fairly well for your intended purposes. The Telstar 28 has a cabin with about 6' of head room, as shown by my crew, who are mostly 6' tall... The boom clears a bimini they can stand under, so the boom isn't a danger to your head. The draft on the boat is only FOURTEEN inches with the board up. It can be beached, and will sit flat if it dries out on a mud or sand bottom. The ama decks would work as a fairly decent work platform for the crab pots.
Generally, shorter boats have lower booms, and less standing headroom in the cockpit and the cabin. One problem I see with your plans is that most fiberglass sailboats won't like the abuse that crab pots will give the deck and topsides.
I am looking for a sail boat to use for crabbing in estuaries and bays in southwestern Oregon. I need to carry up to four persons. A small cabin would be nice, but not essential. No need to sleep on the boat. What is essential is finding a sail boat that I can stand up in to sail and to run the crab traps without worrying about getting my head boomed. I'm 6'2" tall. I've sailed Cal 24s and a couple of 26-30 foot sloops. These are exactly not what I am looking for. Since there are a lot of rocks here, i wouldn't mind an aluminum sail boat--a sailing equivalent or all the aluminum plate power boats used here. I don't need speed. I'm only going short distances for my crabs. I need stability and the ability to negotiate both occassionally big chop and skinny water in shallows from time to time. Never sailed a Cat Boat, or seen one up close, but have read they used to be used by lobster fishermen in the northeast for sailing. I hear they draft about 3 and a half feet. But I've also read about sail boats used in northwest Europe's coastal estuaries that have no bottom keel, but rather have keels sticking out at 45 degree angles from the hull to reduce draft and allow the boat to stand upright on its keels when the tide goes out. The weather here is often cold and rainy, so this is not the place to wear shorts and top siders. Rain suits are the rule. I left Socal and love it here, but all the sail boats I am familiar with are just pleasure cruisers. Southwestern Oregonians seem to just use power boats. I want a sail boat that would serve well as a working crab boat. I have no desire to go over the sand bar into the ocean, as I live on one of the hairiest sand bars in the PNW. It can be trailerable, or not. I just want it as short as possible and still be able to stand up in it and crab. Thanks in advance.