I guess I would be considered a Noahide, and do not practice Christianity. However, I often am asked by Christian friends and coworkers what religion I belong to. I tell them Judaism because I don’t know how to explain to people what a Noahide is. I also strongly believe in what Judaism teaches, and I study the Torah almost daily. I even plan to convert to Judaism someday. Is it a sin to say you are Jewish when you are not? As stated, I do study Judaism, and I plan on fully converting, but I haven’t yet.
I do not think it is wise to tell people you are Jewish before you convert. You might be mistaken as being Jewish which could lead to many awkward situations. I would go ahead with the conversion.