I recently discussed this on another forum. I think your frosted one is Henry Greener, the reason behind this is because my father has a green one which I only recently checked with a uv light and ding dong it glowed to my surprise. The dark green blue is a known greener colour. Ours is unmarked. Also a few years back I discussed this shape with an experienced dealer at the Birmingham glass fair and he said he had one with the Greener trade mark.
It seems there are variations of a dos and at least one or two sizes of cat. So I think the mould may?

Have originated with greener 1870ish then somehow Baccarat made them the baccarat cat is signed but the dog is not signed. The baccarat ones are heavier and better quality, and at a later date 1920-30 Meisenthal made a spatter glass version. There are out of date articles (imo)on them in the. Pressed Glass korrespondant.
The Greener ones are exceptionally rare and also come in Vaseline. I may add further information cheers Mike