The /z/ sound is spelled with <z>. The /h/ sound is spelled with <h> or <wh> in who.
This is a contrast between a voiced alveolar sibilant fricative and a voiceless glottal fricative which can only occur initially. It is not a problem.
Interesting pairs include:
The mean density value is very low at 0.2%. The list makes 15 semantic distinctions, a loading of 58%.
Z head Z's heads zap hap zapped happed zapping happing zaps haps zealot helot zealots helots zee he Zen hen zephyr heifer zephyrs heifers zero hero zeros heroes zip hip zips hips zippy hippy zither hither zone hone zoned honed zones hones zoning honing zoo Hoo zoo who zoom whom zoos whose
John Higgins, Shaftesbury, November 2010.