hidden product, only visable via URL?

I have a webstore up, but i want to be able to bill people at trade shows for a down payment for one of our devices. I don't want it to be listed as a product on the website, but instead to maybe just be able to type in the URL, and then have the person order it, or have us enter all the info for them. That way we can get a down payment on the item, have a record of the sale, but not have it be a public option.

Is there any way to do that? I searched around, but couldn't find any answers, or even really the same question

Thank you,
Justin