So, the solution to not wanting to feel self conscious while saying decidedly simple and inoffensive words, and for task simple enough that people could probably be given a simple sentence or two instruction (choose a word that doesn't sound like another one) and could come up with valid examples (like you just did), is to force them to learn a semi-universal and generic set of mostly nonsense words and names?
I did tech support for years, and any time I had to have someone type out a specific set of characters, it was not hard to just rely on common names, animals, or other extremely common words. The amount of wasted man-years in teaching and testing a phonetic alphabet for such little benefit would be mind boggling. The military has very specific requirements which change the cost benefit analysis greatly (verbal communication during battle conditions, for one), but those don't really apply to most people. It's trivial to come up with something that works well on the fly.