I haven't seen it all the way through, but what about Happy Feet? I don't have any scary memories of Bedknobs & Broomsticks, The Incredible Mr. Limpet, The Ugly Dachsund, the old Dr. Doolittle, that Sammy the seal
movie where the kids hide the seal in the bathtub or any of the Berenstain Bears series. The Jetsons Movie was harmless, too. I also loved I Love Lucy and found that funny even as a small child. The episodes with more physical comedy would probably be very appealing to little kids.
I was an easily upset/scared (still am, really) kid that watched a lot of tv and movies. Mary Poppins didn't bother me at all... neither did the Sound of Music... Alice in Wonderland had some tense parts but the magic/trippiness of the rest of it made it much easier to fight through the few "bad" parts (the same with FernGully, Fantasia, and Benji). I remember always being upset throughout Milo & Otis and The Three Lives of Thomasina but always happy at the end - and I watched them about 1.6 million times so they couldn't have been that bad.
The Secret Garden is like this too... tense throughout but worth fighting through to see the happy end.
I would be VERY fast with the fast forward button with: The Secret of NIMH, Rikki Tikki Tavi, Old Yeller, Cinderella, Bambi, Toy Story (saw this as an adult and that boy even freaks ME out), Monkey Trouble, Fox and the Hound, Dumbo, Black Beauty, or Charlotte's Web (still can't get through all of it OR the book without bawling), Thomas the Tank (saw as an adult & I find it very conformist).
I don't know where to put The Land Before Time. I lovedlovedloved that movie, and it totally devastated me every single time, yet I watched it more than anything else. Unlike the Milo & Otis set I mentioned, I wasn't happy at the end - however, I always came back for more. I guess you'd just have to play it by ear?