If you have a phone, you could get one of those little sticky silicone card holders to hold it.
Even before phones, lots of times I have gone to the parks with only the contents of my pockets. though to be honest, these days, we usually bring water. We have a wat bottle clip strap, but it kind of bangs around. On our most recent trip, we ended up using bags.
These days, the difference between bags and non-bags is fairly minimal, if you are opting out because of the concern over the bag check lines. Most non-bag folks get send through the metal detectors, so it pretty nearly evens out.
Except at Universal. All day at Universal, no-bag is much faster than using the lockers, though park entry is about the same for everyone.