Although I've never been in January, the week I normally go (the Saturday after Thanksgiving until the first Saturday in December)usually has reduced hours as well, at least during the week. But I've never had a problem finding ways to entertain myself, so let me share a few of them!
Shop 'Til You Drop: Head over to Downtown Disney, where you'll find all kinds of shops to explore and food to devour.
Games People Play: If you have passes which include admission to this huge "arcade is so the wrong word" arcade, hit it. You'll find lots of family fun... I have yet to see anyone get on board Buzz Lightyar's Astroblasters and not have, well, a blast.
Clown Around: Sure, it's pricey, but try and take in Cirque du Soleil. You've never seen anything like it... and probably never will again!
Pleasure Island: I know, I know, you say you're not club people. But try The Adventurer's Club for a very fun, very "non-cluby" evening. The entertainment here is completely unique, and you're sure to walk away with a smile.
Under The Boardwalk: Ok, not under it, but on it. The Boardwalk has all kinds of fun things to do, including shopping, eating and the dueling-pianos fun of Jellyrolls.
Dinner & A Show: Take in the Polynesian Luau, the Hoop-Dee-Doo Musical Review.
Explore: I love picking a resort or two to visit in the evenings, and explore to my heart's content. Some in particular lend themselves to nighttime visits. The Animal Kingdom lodge is just gorgeous at night. If you like wandering around checking things out, the resorts are a lot of fun in this regard.
HOpe any or all of this is a little help in your decision!
Richard