I was the same way. I needed the security of my crossbody bag that was full of things we *might* need while we were in the parks. As it turned out, I realized that after 30+ days in the parks, I never needed about 95% of what was in that bag. And the things I *did* need, fit in a tiny crossbody wallet (about the size of the deck of cards) that actually fit in my pocket. However, I probably never would have made that leap if it didn't happen by accident during one of our trips. It was our "down" day and we were spending a few hours at DTD. We had planned to go to one of the parks later that night (after dinner). We had lunch at DTD and then decided we kind of wanted to go to a park that afternoon instead of that night. And everyone wanted to go (indirectly) straight from DTD to a park. I nearly had a meltdown. When I left the room that morning, we were going to DTD for shopping and lunch -- that's it. Then back to the room. I only took our tickets, my ID, a credit card, and a little cash which all fit in a little lanyard pouch I had. How could I be expected to go to a park with JUST THAT????? I insisted I needed to go back to the room first so I could get my park bag. My husband insisted we'd be fine without it and we could buy anything we needed at the park (our kids were 4, 8, 9, 20, & 22 on that trip). I seriously nearly had a full-blown panic attack. But guess what. We spent a few hours in the park and didn't need anything we didn't have in our pockets. And I quickly realized how freeing it was to not have the bag hanging on my body. That was the end of my bag carrying days at Disney. I still have a tiny wallet on a string (because I don't want things to fall out of my pockets) but it's basically big enough to hold my phone, credit card, ID, and some cash and actually fits in my pocket. Next trip I'm downsizing to just a clear pouch that goes around my neck on a lanyard and will hold the same amount of stuff. That's what my DIL used this past summer and she never had to go through bag check since it was small and clear.
I suggest trying a short park trip without a bag and see how it goes. If someone had made me quit cold turkey, I wouldn't have been able to do it. But because it happened "by accident", I was forced into the situation and I'm much happier because of it.