For a woman, wearing a men's watch is something we are used to seeing.
Except if your wife has a large wrist (I would say over 17cm), I would recommand 37mm.
I tried it with my 16cm and it felt great.
However, it depends of what she is used to wearing. If she wears Paneraies, then 39 could maybe be a better choice.
If not, then 37 is good imho.
Very nice gift!