Yes, self-preserving, aqueous products are a thing. Really! But these are typically very difficult to formulate, and you don't put them on a store shelf (including virtual selling platforms) without lab testing to verify that your product truly is good to go. And there are lot of misunderstandings out there about what it takes to self-preserve a formula (like that if your formula only calls for 5% water or less it will be fine - this is not how you measure water activity).
Self-preserving formulas present a unique challenge, and you should go for it if you want to. But go for it with the understanding that you should be prepared to invest in the appropriate lab testing if you are planning to sell the product. This is not an area you skip out on that.
If you make a specific claim (such as a product being self-preserving), you need to be able to prove it. And "proving it" does not mean your "educated" guess. Many assume their products are fine when they are not.