Definately silver lace. All of the chasseur a cheval regiments (except the 27th, which had a Belgian origin) had silver lace on a green uniform. I have seen a few versions of the original print on the right ( by Aubry?) and they show silver lace. There may be other versions though. De Grouchy's uniform dates from 1809, when he was a general, not a marshal.
While the rank of Colonel General was more than just ceremonial, with some administrative duties, I suspect de Grouchy would have worn either an ordinary general's uniform on service, or, for instance when he commanded a dragoon division, dragoon dress with general's lace. There is however a contemporary watercolour of Marshal Davout wearing his Colonel General of Grenadiers uniform, with cocked hat, at Hambourg in 1813.
De Grouchy lost his Colonel General's post during the Restoration, just prior to Waterloo.