A really simple but effective method to create an unintelligble language from a given language is applying a substitution cipher to the vocabulary. In order to be pronouncable, vowels should be substituted with vowels, and consonants with other consonant of comparable sonority.
It is of course a special case of a relexification, but is there a specific term for this?
"code" or "coded language". Probably mostly used in conjunction with sign languages, where the signs replace the (spoken) words (e.g. Signing Exact English as opposed to "natural" signed languages), but also for "encoded" spoken languages (either by relexification or phoneme substitution).
I have never heard of a "substitution cypher language."
One might adduce Pig Latin or Double Dutch as examples of such a thing, but these are not conlangs. They are typically called "language games." A substitution cypher is not a language--it's a way of disguising one or more languages.
To qualify as a conlang, a constructed communication system has to have its own grammar and its own way of mapping meanings onto words.
I think we could use some terms from physics here. Let's say a relex is isochor (alternative: isomek from Ancient Greek mêkos "length") if it preserves length of words, and isotonic (alternative: isoson/isosonor/isosonic, a Latin-Greek mix) if it preserves sonority patterns. Your substitution cipher would then be an isochor-isotonic relexification.
