I don’t want to discredit this, since I don’t know your source, but linguistically that seems quite unlikely for a consonant introduced three thousand years ago to have influence on the modern Cornish place names. Three thousand years ago, the Celtic languages hadn’t even split from proto-Celtic, so any influence on Cornish should have also had influenced on the rest of the Celtic languages. In addition, the sound /z/ is a very common one across languages (so it does indicated Phoenician influence), and they didn’t have a script then to write the place names (so the orthographic letter z doesn’t mean anything).

I’m not an expert so forgive what might be a naive question.

Even if the languages had not split, could there still not be regionalised influences on place names?

That’s true, but the long time change leaves it quite unlikely that the names would leave enough of a remnant of a particular sounds that you could point to a Phoenician influence.

Can you point me to the information sources for this theory?