You can always have the reception there and have the ceremony in a church or someplace else off grounds.
I do know that Disney is not a big fan of "Gurella Weddings"
You also could rent one of the larger available watercraft and hold the ceremony on the water.
Those are the only two scenarios I could imagine where you'd have about zero chance of anyone stopping you. Otherwise, you're looking at holding the ceremony in some non-descript, out-of-the-way backwoods section of property (which defeats the whole point of getting married at Disney), or doing a very quick exchange of vows with an officiant someplace in a park. That you could get away with just about anywhere, provided you're not blocking a pathway or entrance.
If you really want to do a ceremony in the park with more than a couple people, or one that lasts longer than two minutes, I'd consider Tom Sawyer Island.
Still, resorts like the Boardwalk, the Beach Club, and the Contemparary have rooms in which you can have a lower key wedding without the whole Disney fanfare.
Personally, I saw one at the Boardwalk when I was there in a Gazebo on the way to EPCOT. Very nice and small! I would look into that!
The cheapest official Disney package is the Memories Collection, which covers a ceremony, flowers, limo, violinist and photos for a gathering of four guests, plus the couple. That's $1,900.
I got married at WDW 5 years ago, and let me tell you, it was the best dam $&^$*(*^%*^( I ever spent (I won't tell you how much it cost - it was more than it should have been for a ceremony and reception for 30, but it was Disney). We're still paying it off - no one paid a dime for it but us, and I'll never regret for one second every fabulous minute we spent in the Wedding Pavilion, on the Grand 1, and in the Napa Room at the California Grill watching our own personal fireworks show (Wishes... but it felt like it was just for us). As the t-shirts I made myself to wear that week said - Better Debt than Regret. We're even thinking of doing a 5 year anniversary vow renewal this year with that Memories package - that's how much it meant to us.
If you're serious about it, look into it. They'll far exceed every expectation you could ever have. And no, I don't work for Disney Fairy Tale Weddings... :-)
- Jill - Happy Disney Bride
Walt Disney World
Tokyo Disney Resort