I've seen hot dogs that were labeled "Uncured Beef Hot Dogs" and the label states things like "Not Preserved" and "No nitrites or nitrates added", with "added" as the key word. However the ingredients list "Cultivated Celery Powder".
Look into a product called EcoCure #1, and #2. It's made by The Sausage Maker and for now... it's alternate for home curing. It has not been approved for commercial use yet. Two Guys and a Cooler are using it in some of their videos. Very pricy.
Funny you should mention vegetable juice cured hams. I use an injectable curing brine with a vegetable broth (Kitchen Basics brand) but it has phosphates, Cure #1, salt and sugar. In a nutshell you inject an amount equal to 10% of the meat weight, then cure for 12 to 14 days. Here is a ham from a pork butt, and the shoulder picnics are just as nice.
If you use some sodium erythorbate along with the cure#1 you can cut the cure time down to 12-24 hours.