ABSOLUTELY NOT!!! Nintendo would never share a core franchise with a competitor.
Actually, if there is a Wii U or Switch emulator for the PS4, then that would work. However, I’m not sure about the state of such emulators or care to research them.
Another thing to consider, Genshin Impact is coming to the PS4, and although I’ve heard of the differences between the two games, comparisons have been made.
But yeah, Zelda will never be on any non Nintendo console (excluding the horrible CD-i games). All of Nintendo’s characters will stay Nintendo (and recently, cellphone) exclusive until at least 2090.