L.B.
Vaseline! Just get some cheap-o, no-name brand from dollar tree and slather all the parts you've cut with it. It will keep a LOT longer. The only thing I've found that's a little gross is that it does attract little flies if the weather is still a bit warm, but no one really sees that part but you.
It's worked for me the past couple of years (yes, I don't have kids yet but I carve my pumpkins every fall!)
Happy carving!