Like anything else, use your head--and your eyes--and you'll be OK.
The marked shipping lanes are a good start, but don't depend on the ships to stay there. You'll find freighters, especially the small ones, well inside the lanes at times running west along the beach.
Be careful in the fog. If you don't have radar, think twice about going anywhere near a place where there might be ship traffic if visibility is poor. I can tell horror stories about being out with folks in the fog, when it came in so thick that you couldn't see the close-in float on the shark rigs. And then you hear the engines, with the big props chugging slow, until you can hear the sound of the water sliding up along the ship's hull--but you don't know where it is. The captain of the small boat has turned the engines on, and is staring toward the sound with his hand on the controls, hoping that if the sharp gray line of the vessel's bow comes towering out of the murk, he can goose the outboards and get the boat out of harm's way before it's smashed under, but you don't really know if that's true. And he doesn't want to move the boat before he sees anything, because he could just as easily be moving it into harm's way as taking it to safety. Then the sound of the engines crescendos--you swear that you can hear the bubbles of the wake boiling up--and just begins to fade away before the wake hits, an you hold on as the boat pitches, knowing that this time, you got away with it...
Remember that a fiberglass boat is a poor radar target, and won't be picked up until the ship is close, and by that time, the little boat may be in the shadow of the ship's bow, in a blind spot where neither radar nor human observers can see. Remember, too, that until they are close to harbor, ships often run on autopilot, and there may be no one in the wheelhouse standing watch. There was a classic incident out on the Bacardi wreck on the night of July 31/August 1, 1989, when a big freighter far from the marked shipping lanes plowed though a tuna fleet comprised of well over 100 boats--maybe double or triple that number--anchored on and around the wreck, many with crews completely asleep, and it was only thanks to the alert eyes of a handful of anglers, and their timely warnings, that kept anyone from being killed, although there were some very close calls. I had friends out there that night that are still spooked by the memory, one who was close enough to read the big print on notices on the wheelhouse bulletin board as the ship passed by.
If you anchor anywhere near the lanes, even on a clear day, use an anchor ball that you can cast free if you need to move in a hurry. Remember that it's not only the big ships that you have to worry about; seagoing tugboats and barges often pay little heed to the shipping lanes, and are quite common as they run along the coast. Such vessels offer the operators little visibility, so always assume that you are the one who has to move. If you're drifting, don't be slow to move if you see something coming. If you're trolling beyond sight of land, make a pass a few hundred yards behind the ship, crossing its wake; tuna are sometimes drawn up by the commotion, and you may get your only hits of the day--but don't come so close that you might be seen as a threat to the vessel, and stay well clear of Navy or Coast Guard ships, or anything that might be carrying flammable cargo--they're pretty protective about such boats.
The bottom line is that you're far, far more likely to be done in by a drunk in a Sea Ray than by any of the big stuff moving outside. But keep your eyes open anyway.