POD to the others. Aside from the rule about not including any kind of gift information in the wedding invitation, I would also be totally confused to find a travel agency business card there, with no explanation.
If you don't do a website, that's fine. You can wait until people ask you what you want, and after saying that you really have everything you need, if they still want suggestions, you can say that you're going to location X for your honeymoon, and that you've registered with a travel agency for the trip. I've actually never heard of registering with a travel agency the way you would at a store, so it wouldn't have occurred to me that this exists. I've heard of honeymoon funds, but I guess I didn't realize that was how they worked--usually it's described as being directed to the couple's website. Does the travel agency have a page just for you two with purchase info? That's the website you could give people, when asked for further info.
You might also consider ideas that are related to the honeymoon location, but don't involve directly contributing to the honeymoon fund, that you can tell people when asked, or even register for. Pretending it's a tropical beach--light beach reads, sun protection gear, new luggage, flip-flops and cover-ups, beach towels. Even gift certificates to specific stores/restaurants at that location (which are also available easily from a distance). Basically stuff that you would have spent money on anyway or that would be really nice in the context of the honeymoon.
You could also register for stuff you'd just like, books or DVDs or whatever. I know some people don't find that kind of thing "wedding-y" enough, but then they could choose between a wish list of books, contributing to the honeymoon fund, or doing something on their own.
To me, the thing with a honeymoon fund is that it's basically just... giving money. Which some people are fine with and might have done anyway, but that's only giving your guests one single option of a thing to give you, unless they go totally off on their own with little guidance. It's like registering for 100 identical blue bath towels or something. "No really, that's all we want. We love these blue towels." Actually that would be kind of funny...