By foam, do you mean soft foam or rigid pink or blue construction foam?
If soft foam, you could use large-diameter pipe insulation but I dunno about how well it would take paint. Maybe you could coat it with adhesive-backed vinyl instead.
If hard foam, I suppose that you will coat it with epoxy, and possibly also fibreglass in places.
Then I propose that you make the barrel in epoxy/fibreglass in two parts. Fibreglass can be really thin and lightweight, yet hard. Mould each part inside a halved pipe of larger diameter, coated with a thin layer of vaseline or just simple shrink wrap.
Weak man's option: That looks like an oversized Nintendo light-gun. Your client wouldn't be happy with a real Nintendo gun with the red (or grey) parts painted pink?