Although the ability that Hitmonlee utilizes most often is Limber, to block paralysis, its other ability, Reckless, is also very viable. Despite the fact that the only recoil move Hitmonlee learns is Double-Edge, a 144 Base Power move coming off Hitmonlee's Attack severely dents many of its common counters, such as Uxie. Hitmonlee can use Double-Edge on the Choice set or the Life Orb set. Just try to avoid being paralized
Just an FYI, Hi Jump Kick is boosted by Reckless as well, but it's only as powerful as Close Combat without perfect accuracy. The only problem I can see with using Double-edge on Hitmonlee is that it has low HP. It will lose almost half its health by killing a max HP Uxie with Double-edge.