OP, can you tell us a little more about what specifically you're nervous/scared about? If it's physical safety, I'll agree with PPs, take your usual common sense precautions, but I think WDW is probably one of the safest vacation spots for a solo. If you're concerned about being lonely - I'm used to doing things alone in my regular life and am a big ol' introvert, so I enjoy touring solo, but I know other people thrive on companionship and would be unhappy without it. Only you know where you fall on that scale. If you're feeling awkward, try not to (easier said than done, I know). As others have said, other guests are busy with their own families - and frankly, who cares what they think, anyway? And I guess, the ultimate answer is, you'll never know if you like it until you try.
I love character meet & greets and have done a lot of them. Characters (and their handlers) are awesome. I DID get a comment once about being a solo: Merida excitedly asked me if I was "enjoying a day of freedom!" and she thought that was great.