I just got my first Valentinos as well - I usually wear a US 9, 39.5 in most designer shoes, and the 39.5's fit me very well. You can probably go with a 37, but keep in mind that d'orsay styles like this one usually run a little bigger than the rest of a designer's line, so for this style a 36.5 might be best. But since it's NM, you can always return, so go for it!
I recently bought my first pair of Valentino d'orsay pumps. I am a true 8.5, normally wear a 39 in designer pumps and I bought my Valentinos in a 39. I think they should be fine but NM is great with returns if necessary.