The /z/ sound is spelled with <z>. The /w/ sound is spelled with <w> or <wh>. The contrast can only occur initially.
This is a contrast between an alveolar sibilant fricative and a bilabial semivowel, both voiced. It is not a problem.
The mean density value is very low at 0.2%. The list makes 13 semantic distinctions, a loading of 57%.
Z wed Z's weds zee we zee wee zees wees zees wheeze Zen wen Zen when zest west zinc wink zing wing zings wings zinged winged zip whip zipped whipped zipping whipping zips whips zither whither zither wither zithers withers zoo woo zoos woos zoom womb zooms wombs