I wear a hardhat in an industrial environment where snagging isn't a real big concern. Seem to me that anything you add to the outside, like hooks, is going to increase the likelyhood of getting snagged. How about using adhesive (maybe 3M Super 77 spray or brush-on rubber cement) on the inside of the band to keep it next to the cap. The adhesive would have to be recommended for use on rubber. It doesn't have to be solidly bonded, just sticky enough to make it difficult to get a finger under. Drilling mounting holes can weaken the cap and some glues will make the plastic brittle.

*edit* - OR... how about covering the strap with a layer of our dear friend, duct tape.