No, the sound change m>w is not otherwise attested, and with has a clear etymological relationship to Proto-Germanic *withro, which is also reflected in things like (slightly archaic) German wider “against”.
the sound change doesn't have to be otherwise attested. that is a general feature of nouns and more heavily focused on words. mid/with are conjunctions, almost exclusively rapidly pronounced with little emphasis on their consonants, easily becoming corrupted and merged and changed without the need for general language shifts
> the sound change doesn't have to be otherwise attested.
Somewhat counterintuitively, historical evidence shows that most sound changes are regular! Which means they affect all words satisfying the same condition in the same way [0]. Irregular sound changes still occur, but if you look at the history of a language, regular sound change suffices to explain almost all developments.
Focussing on the history of English (which is very well documented, e.g. [1]) shows this well. Consonantal changes tend to be very regular: for instance, final /ŋɡ/→/ŋ/ in most dialects. English has an unusually complex vowel system, so vocalic changes tend to be somewhat more chaotic, but still show regularity: e.g. /a/ regularly turned into either /æ/ or /ɑ/.
It is true that very frequent words (whether nouns, prepositions, conjunctions, or whatever part of speech) can undergo one-off changes, usually involving dropping syllables. But the phonetic details don't make sense here as a reduction: with is arguably harder to pronounce than mid.
You're basically arguing for a rare and poorly understood kind of lexical change with no evidence to support it, against a well-understood and very common kind of change with multiple different strands of converging evidence.
It's not impossible that the phonological similarity of "mid" and "with" made it easier for the meanings to coalesce in "with". But it is certain, at least as certain as you can get in historical linguistics, that these were originally two prepositions with independent origins.
