I don't think there really is any non-shedding dogs apart from the Poodle and the Yorkie ... but I hope we agree that a dog can hardly shed less than an Otterhound. 

The care of the Otterhound coat is fairly straight forward as the Otterhound is not being trimmed.

The optimal way to deal with the coat is to brush it through thoroughly once per week (preferably when dry). Not to forget the beard, the tail and those hard to reach areas on the tummy and the inner legs, done...
If this is done regularly and any bits and pieces as well as ticks are being removed straight after a walk than you will find that the coat won't get matty. However, should there be a matted part after all you can try to remove it with a trimming knives or take the scissors and snip it away....
After all, it will grow back.
A bath should only be given if the dog really smells bad because he rolled in something unpleasant etc.!
Washing a dog with shampoo is not the ideal thing for the waterproof undercoat and should therefor only be done on rare occasions.

 

What to do if you want to show your Otterhound:Well, of course the coat should be lokking well looked after, so you should remove matted parts of the coat, but do not trimm your Otterhound as this is not regarded as a natural looking coat and points will be deducted.

If you decide that you wish to bath your Otterhound before a show than I would advise you do so a few days before the date of the show as the coat is to have the slightly oily feel which it may not have if bathed shortly before the show.