When we went in October with our friends, they have a not-quite three year old who didn't like ANY characters. Toward the end of the trip we were at AK and there were characters out front. Nancy and I each took a hold of John's hand and we approached Baloo (the character, not the moderator

). John walked with us slowly and I yelled that sorry Baloo, John is afraid. Well, Baloo sat on the ground (not an easy feat for a big guy) and waved to have John walk over slowly. Because we've been to Disney before, I understood some of the gestures that Baloo was making. He asked John to feel his fur on his hand. John let me stroke Baloo's hand with John's hand tucked in mine. All the while I was speaking softly to John:
See John, he has soft fur. Then Baloo wanted to touch John's hand and I said "do you have soft fur like Baloo?" and John laughed because he knew he didn't. We actually turned a corner with that visit. He got a little closer and shook his hand at the end. On the last day John actually hugged Mickey and said Bye Mickey!!
The point is that the characters are used to children being afraid. Try to find one that has no line and you will be surprised to see how well they handle it. I would recommend that you go up and spend time with the character so that Alyssa will see that you are not afraid. Don't push her at all - by the end of the week she may be ready to say hello to one of them. If she realizes that nobody else seems to be afraid, she may try (or may not try) to socialize with them. But think about it -- its a big furry thing, probably twice or three times her size. I'd be afraid too!!!