I'd be a bit wary of adding a zero fret as you've got currently no fingerboard to add it on to. You'd need to fabricate maybe 5-6mm of extra fingerboard with a matching wood to fit the zero fret on. That moves the nut back by a similar amount, which exacerbates any string splay and also makes it awkward to fit the nut as the headstock in that location is both splaying out as it widens and sloping down, so the base needs to be angled. It can be done, but it's quite hard work to do well and is pretty much an aesthetic issue. I'd certainly make any zero-fret from stainless fret wire so it doesn't wear out so quickly.

I'd keep it simple and just replace the nut as-is.