Writing the names of both people on the invitation should be fine.
I'm not sure if this is an Midwest thing or not but we would say something along the lines of "cake and coffee will be provided" every invitation for birthday parties, engagements and work get togethers has just had that written on it but then there is also always cake and coffee.
But I don't think you ned to mention food.
I think most people will assume there will be food at the shower and even if they do eat beforehand, they'll eat again. Ever been to a Costco on a Saturday? People don't say "no" to free food. I think the mention of men and women does need to be explicit, since most people won't even really notice how the invite is addressed.
And I'd still expect a few wrapped gifts: it's a concept most people won't be familiar with.
As for the presents you could say something along the lines of: "in an effort to be more ecofriendly we ask gifts be left unwrapped. We will be accepting gifts at the door to leave more time to party!"
Naming both people should suffice, but you could also ask people to rsvp with the number of guests who will be attending to drive the point home.