I'm aware of three. There's a very small plastic kit by Academy: http://www.academy.co.kr/eng/1p/1p_plaview.asp?pView=PLA0000006&pCode=542&pScale=SCALE00001 . I think it's a reissue of an ancient Pyro kit. It's quite small, and basic, and has some obvious errors in terms of accuracy, but if you have the itch to build a whaler in a hurry this one may satisfy it.
Revell used to make an excellent Charles W. Morgan. It originated in 1968, and reappeared briefly a year or two ago in a Revell Germany box. The Revell Germany website doesn't list it now, but I suspect it could be found with some searching. It's on a pretty small scale (about 18" long), and it has a couple of problems that ought to be noted. One - it represents the ship as visitors to Mystic Seaport saw her in the sixties - with a single-topsail, full ship rig. She is now rigged as a bark (as she was in the latter years of her whaling career), and a recent major restoration has changed a lot of details. Two - the whaleboats are problematic. Their hulls are beautifully shaped, but only two of them have details in their interiors. The others are supposed to be hidden under vac-formed "canvas" covers, which no working whaleboat had. (Those boats were crammed with masts, sails, oars, harpoons, line tubs, etc., etc.; there's no way a canvas cover would work.) But it's a very well detailed kit, and quite accurate - if you want a model of the Morgan as she looked in the sixties.
Then there's the Model Shipways version. It's a plank-on-bulkhead wood kit, and quite expensive: http://www.modelexpo-online.com/product.asp?ITEMNO=MS2140 . It's a highly advanced project, intended for people who have plenty of experience with wood kits under their belts. An experienced modeler probably would need at least a couple of years (part-time) to do it. It's highly accurate, having been designed with the collaboration of the folks at Mystic Seaport. (One small reservation about that: I'm sure the recent restoration changed some things from the way the model depicts them.) A member of our model club built one, and it's extremely impressive.
Model Expo's website (see the above link) gives you the opportunity to read the instruction book, which will give you an idea of what you're getting into if you buy that kit. It's a fine kit, but one of the worst possible choices for breaking into wood ship modeling.
So far as I know, that's what's currently available. Marine Models and Scientific used to make somewhat simpler wood whaler kits, but they've been out of business for decades.
Bluejacket and Model Shipways both make wood whaleboat kits; those also are advanced projects - and not cheap.
The unfortunate truth of the matter is that the available range of plastic sailing ship kits is so small that it doesn't even scratch the surface of the history of the sailing ship. It seems like a 1/96-scale whaler would be a natural. But none of the manufacturers has shown much interest in sailing ships for the past thirty years or so.