There are flexible resins but man after looking at that part i would not get my hopes up. I have designed foaming soap pumps that use very thin walls to seal the liquid from the air. We had to go to prototype molds.

That is where companies like protomold come into play. They have an auto quoting process and can turn molds around quick. Standard turn around is 3 weeks from order to parts but can be expidited down to a week. Then you can tweak that mold before comiting to hard multi cavity molds.