The first solo visit I took two years ago I had some of the same concerns you have. To combat them I decided to jump into the deep end of the pool and made reservations at CP in MK for dinner with Pooh and Friends. I figured if I could make it through a character dining experience without folks looking at me like a whacko, or worse, then I would never worry about it again. I brought a book with me just in case.
It turns out my fears were unfounded. The CMs made sure I had photos with all of the Characters and even had Tigger come back over when one of them saw that I had a Tigger tattoo. Two tables near me talked with me during dinner and had no concerns about a lone male in a Character Dining experience. They also helped me take photos with the characters. Since then I have had at least twenty-five solo meals and only twice have I had funny looks. I just smiled at those people and went on with my thing. I have found that a lot of other dinners will engage with you when you are dining alone if you make a joke or just ask a question. One night I had a two-hour conversation about Brexit and other political subjects with a couple from the UK, I told them I felt terrible about monopolizing their time, but they said they enjoyed the conversation and had a good time.
There have been meals where I just sat there and ate while not interacting with anyone but the CMs. To me, that's okay too. The key, I think, is not to worry about it and enjoy yourself and the food. Do you care what other people, who do not know you and you will most likely never see again, think?
All that being said, when are you going? If I am there I would be happy to sit with you and enjoy a meal and conversation!
-Frank