You've been cheated of your diacritics, and proper etymology with them. That's /Ž/, which sounds like /Dj/ in djinn or /g/ in ginger. All the consonants are soft, stress is on the base, spelling is "žynystė" and "žynė" respectively. Semantics is a bit off too: 'žynys' is more of a prophet or a witch doctor than practitioner of sophisticated magics. Sadly, I cannot show how this is relevant to the origin of 'wizard'.