I've been a baby wearer at the World for two years running now. Two years ago, I carried our littlest one in a front carrier. He was 6 months old at the time. This past year, I carried him in a backpack. He was heavy, but it was so worth it. In both instances, near nap time and later at night, he'd check out. The last thing we'd want to do is wake him (and/or leave the park!)
We never had a problem wearing him onto slower moving rides. While each situation is unique, I can tell you that I've worn him (backpack and/or Bjorn) on the following:
Jungle Cruise
Pirates
Magic Carpets (Bjorn)
Swiss Family Treehouse
Small World
Haunted Mansion
Peter Pan's Flight
PhilharMagic
Dumbo (Bjorn)
Many Adventures of Winnie the Pooh
Teacups (Bjorn, probably not good for a 3 week old)
Buzz Lightyear
Journey into the Imagination
The Seas with Nemo and Friends
Living with the Land
Kilimanjaro Safaris (might be too bumpy for a 3 week old)
Triceratops Spin (Bjorn)
Toy Story Midway Mania
Great Movie Ride
You can even wear your 3 month old on the Disney Transportation System busses. Make sure to take advantage of the rider swap option too - you and your hubby can take turns riding with your kids while one waits with the baby (and your older kids get to ride twice!)