There is (or has been) a fairly popular TV show called "The Most Dangerous Catch" or "The Deadliest Catch" which is about fisherman going after Alaska King Crab. It is mostly the weather that can make the job very difficult and dangerous.
Well, who said the fishermen have to be on top of the water
to do their job? It is well known that however stormy the surface is, an underwater vessel located, say, 30 meters down, will barely be affected.
So, we start with a basic submarine design. Note that for surface vessels there is a peculiar dividing line between calling it a "boat" or calling it a "ship", but all seamen always call subs "boats", no matter how big they are, so we will definitely be describing a "crab boat" here.
If the normal operating depth for this sub is say, 30 to 50 meters, then it should be possible to use that well-known device, the snorkel, to obtain air from above the surface. Access to air means that diesel engines can power the sub, instead of batteries.
Most subs have a double hull, so that the space in-between the hulls can be used to hold air (make the sub rise) or water (make the sub sink). We can still do that here, except that in at least one place at the bottom of the sub we need an opening through the double hull, to allow direct access to the water, from the interior of the sub. I'll get to the main side-effect of that in a moment.
It is through each such opening that a crane can lower or raise crab cages. This crane should be located at the inside-top of the sub, and the opening should be more like a "well" through the height of the sub, than just a simple opening at the bottom. The "well" design means that as soon as a crane lifts its burden out of the well, and shifts horizontally, the burden can be dumped into the body of the sub next to the well --the body of the sub is mostly "hold" space. It is only the topmost level of the sub where the crew would live and operate the sub.
Another advantage of the "well" design has to do with overhead waves. If a 20-meter wave passes over the sub in a surface storm, the water pressure on the sub will increase temporarily, and the water in the well would rise. A nice deep well would ensure it never rises above the top of the well.
The main side-effect of having direct access to the water, from the interior of a submarine, is that the air pressure in at least that part of the submarine must be increased significantly, to keep the water from entering the sub through that hole. (Most subs normally operate at sea-level air pressure in their interiors.) For a normal operating depth of 30-50 meters, this is not a big deal; the human body can accommodate such pressure easily. However, it does mean that before the fishermen can leave the sub, a period of slow decompression will be necessary, to prevent "the bends".
Note the preceding paragraph implies that not all of this special crab boat needs to be pressurized. If there was an air-lock between each crane/well room and the rest of the sub's crewed area, then only the crane/well room(s) (and the hold) need be pressurized. Decompression would still be necessary; it would simply take place in the air lock. I tend to think, though, that the overall danger would be reduced if the whole sub was pressurized, and decompression only happened once per crabbing trip (at the end).