I don't see any difference between both. It simply depends on the context. None of them is more formal than the other. On a side note, with a native english speaker, you wouldn't wanna use such an expression as "I would be blind". It might sound a little unnatural. Also the tense you chose here "Future Simple". It would also sound more natural if you used a conditional instead. I would just go with : "thanks for letting me know, otherwise I would have done so and so" Check this page out, might answer your question! https://idioms.thefreedictionary.com/or+else I hope that was clear. :)

Otherwise is not formal or informal as far as I am aware. I hear and use it often. I am a native English speaker from the USA.