From what I gather the prohibition on the production of images is a Mosaic law, so are Bnei Noach exempt from this?
Noahides are prohibited from making, or using, idols. "An image of God" doesn't really work, because God has no image. And if someone suggests they'll make a statue of an imposing-looking male (or female, for that matter) figure only as a symbol to inspire people to pray to a non-corporeal deity, well... that's an incredibly slippery slope to idolatry.
But let's stick with something safe! Decorative or commemorative statues!
Shortly after President Kennedy was assassinated in late 1963, the mayor of McKeesport, Pennsylvania decided that his town should have the first statue of JFK in his memory. He asked Rabbi Chinn to be on the planning board and help raise funds for it. Rabbi Chinn consulted with Rabbi Moshe Feinstein, who replied in January 1964 -- the responsum is found in Igros Moshe Yoreh Deah II #54. Rabbi Feinstein explicitly allows it for your reason -- non-Jews aren't prohibited from making, having, or using statues that have nothing to do with worship.
Now making a statue in the image of man, even for decoration, is prohibited – whether to make them or to have them (when made by a gentile for him), as is ruled in Shulchan Aruch YD141:4. … however non-Jews are not commanded in the prohibition against making a statue for decorative or political purposes. Though we need no proof to this as it is not in the seven [Noahide] commandments, it can be proven from Tosafot … and thus it follows that it is not prohibited for a Jew to assist a non-Jew in his making of a political statue, or even to assist him financially, as for non-Jews this is a permitted act.
(He also points to R' Akiva Eiger, Rosh Hashana 2.11.)