Hi,
I am not an expert but I agree with you, from the shape of the leaves it definitely looks more like a Zelkova Serrata.
About Zelkova Nire vs Ulmus Parvifolia, I have to say that I still can't tell one from the other…
I have 2 Zelkova Nire and 1 Ulmus Parvifolia myself (so they were labelled), and they look perfectly identical…