Answer: Hatzlacha on your new venture.
This is a fascinating and difficult question. On one hand, assuming there are metal pieces coming in direct contact with the food being prepared, there should be an obligation to toivel it miD'Oraisa. Furthermore, unlike kashering where the primary concern relates to the impact of the utensil on the food, which would not be an issue when it is anyways not being sold as Kosher, tevila is different. Since the primary obligation of tevila is incumbent upon the user prior to his usage of the object, it should be irrelevant who the customers are. In this case, since a Jew, you, are intending to utilize this equipment, it should require tevila.
However, the Shulchan Aruch Yoreh Deah 120:8 provides that only usage for preparing or serving food obligates tevila, but a knife designated for cutting paper is exempt. The main question would be if we can classify preparing food exclusively for non-Jews as an exempt usage. I had the opportunity to present this question to HaRav Zalman Nechemia Goldberg (HaRav Shlomo Zalamn Auerbach zatzal's son-in-law and the former Av Beis Din of the Rabbanut's Beis Din HaGadol) last week, and he found this logic a likely possibility. Unfortunately, we were unsuccessful in locating any source for such a distinction, and he was unwilling to commit to accepting the classification of solely gentile consumption as a non-food usage that would exempt it from tevila. He repeated a number of times "It sounds good, but..." Even when I pressed him to take into account the Poskim who consider an electrical appliance an exempt item due to its connection to the ground, he remained noncommittal.
In conclusion, it seems that you must toivel whatever parts of the machinery are obligated in tevila, but certainly without a bracha. Certainly, if you expect to occasionally eat the frozen yogurt yourself relying on your personal knowledge that it is truly Kosher, you are absolutely required to toivel it. If you wish to know which specific parts require tevila, you will have to send me a diagram or photo of the machine.