I would look at a private label with a major player in the market. You are correct in that most retailers do not like to carry one SKU from one vendor. Having said this, if the product is a good product and the buyer feels that the pull through numbers will be adequate, I have seen drug store chains carry one SKU but all in all its awfully rare anymore.
You are responsible for having a upc and a Dunns number. This is essential to selling your product to any major retailer. They will look at your dunns report to make sure you are not a finacial liability. You will also need to purchase liability insurance before a buyer will purchase your product. I know that everyone says its hard to get a buyer to purchase a one item problem and it is true because of the cost involved in setting up a vendor with only one product. If the buyer really likes your product, they will either purchase it directly or send you to a distributor they deal with that will purchase your product. Don't worry about having a one item product, just get the meeting and get the buyer interested in your product and the rest of the process will take care of itself.
Visit my site for more information about selling your product to major retailers and distributors.