I've been to WDW several times solo (and will be solo again next week as my friend cancelled at the last minute). There is nothing I wouldn't do by myself. Highlights have included:
Riding "Expedition Everest" with a mom who ended up on the single line. We had a blast and we both realized that we were too old to be riding a roller coaster backwards.
Sitting next to a "grandma" on "Soarin'". I am afraid of heights and actually had a panic attack. She ended up putting her hand on mine saying "It's OK, Dear."
I will be riding Toy Story Mania by myself, guaranteed.
Maybe it's me, but I truly don't mind being by myself. I can set my own schedule. I've met interesting strangers and I can look at all the pins I want to!!
Go, have fun! And don't be self-conscious. Even if someone else does care what you are doing, ignore them! Why let a complete stranger ruin your vacation.