Personally I pronounce "prince's" with a soft /z/, but it may be up to personally preference.

It's has to be a /z/ sound. We have no choice in this matter. 'Princes' is pronounced /'prinsiz/ with the stress on the first syllable. 'Princess' is pronounced /prin'ses/ with the stress on the second syllable. For the native speaker, these are very different words. Practise them and see.