Though Hanazawa was able to read Shimazaki's moves, I think they aren't as easy to read as Hanazawa said for a few reasons. First, Hanazawa had already fought Shimazaki once before, and the second time, he had an army of several of the 7th division's top espers helping him, and even a few extra Scars to help in the manga. Fighting as a group allowed Hanazawa a much easier chance to study his movement patterns and figure out where he'd teleport. If it was just him fighting Shimazaki for Round two, I doubt it would've gone as well as it did.
Deku's advantages here are his higher AP, 5.13 tons, his incredible stamina, and his analytical mind. Even if he doesn't have the same analytical prediction as he did in Shie Hassaikai arc, he could still probably figure out Shimazaki's movements, and Shimazaki's biggest attacks probably wouldn't be too bad to deal with, since 5% Deku has endured large impacts with metal constructs. So eventually, Deku would have a better time reacting to Shimazaki's movements and potentially counterattack. However, Shimazaki would eventually he'd need to step it up and activate his Mind's Eye.
Mind's Eye doesn't apply solely for espers. It's just that the one time he used it, Shimazaki chose to focus only on espers. If he chose to focus on something else with Mind's Eye, the same would apply. On his profile page in his weaknesses section, it doesn't say, "Super Sensory "Mind's Eye" only works on espers." It just says, "Super Sensory "Mind's Eye" makes him unable to sense whatever he doesn't focus his 'antenna' on." Reigen was able to surprise Shimazaki because he wasn't an esper and Shimazaki's senses were only focused on predicting the moves of espers. So if he focused his antennae on Deku, he's be able to better read his movements and his weak points. Now Deku might still be able to keep on fighting even after that, but I think he'd be too weakened to put up any real struggle.