I’m mainly talking about conversations that are wired (like those use by law enforcement) when an undercover agent is wearing a wire. Of course, those conversations are recorded but can languages alone obfuscate the nuance of the spoken dialog since each language is different?
Again, not talking about “Spanish to English” level translation where it’s straight forward, rather it’s closer to “Japanese to English” where there are cultural differences, slang, honorifics and personification that can’t be translated properly without given context in advance.
The use of Navajo worked because the Axis countries, including Germany, trying to decode were not aware of the Navajo language and were trying to decode it into English/French/etc.
A constructed language is just about the only possibility, but we can translate dead languages up to a point and someone trying to create a language is likely to end up with a structure close enough to make translation trivial.