a)pokru/ptein: w(/ste me e)mauto\n+ a)nerwta=n+ u(pe\r tou= xrhsmou= po/tera decai/mhn a)\n ou(/twj w(/sper e)/xw e)/xein, mh/te ti sofo\j w)\n th\n e)kei/nwn sofi/an mh/te a)maqh\j th\n a)maqi/an+, h)\ a)mfo/tera a(\ e)kei=noi e)/xousin e)/xein. a)pekrina/mhn ou)=n e)mautw=| kai\ tw=| xrhsmw=| o(/ti moi lusiteloi= w(/sper e)/xw e)/xein.
P.A. 22e

Why does Plato use "mh/te" with the participle "on" instead of "oute"? The participle definitely has no conditional or general force.

I think both can be used without problem, synonymously, but check it further and let us know if you discover anything.

Vir litterarum : In Smyth's Greek Grammar, #2942 is headed "oute (mhte)". The discussion there indicates interchangeability. Two examples from Plato don't clearly address your question, though. Beyond this, I'm out of my depth.

"oute" and "mhte" are definitely not interchangeable. Their usage corresponds to the difference in usage between "ou" and "mh." Someone else I know suggested that "mhte" is used because, if "echein" were negated, "mhte" would be used (examples of this are listed in Smyth 2737c), and this explanation seems to be the correct one to me.

"Seems to be the correct one to me" is not enough, especially when a search in Plato would prove you that oute and mete are used synonymously. There is, though, a general difference in the words me and ou, the latter being a more certain negation, since me can also have the sense of "maybe". This 'side' of its meaning may have at times some influence in its negative use as synonymous to ou, but this is a matter one needs to investigate.