Learn English – Is it correct to say: ‘I wish I would (not) do something!’

Per my comment, I'd avoid it because it sounds rather dated and "upper class" to me.

Semantically, the reason for avoiding this construction is simply that it takes the focus off the critical word not. Since the "conclusion" clause is intended to convey something along the lines of "I am failing", this negating word is vital to the sense.

In "injunctive" forms, such as "You must/mustn't do that!", the word must is invariably stressed, to emphasise the intended meaning. In OP's usage, the word must wouldn't normally be stressed, because there's no sense of injunction or stricture (except loosely, in the sense that there's a logically enforced conclusion). It's "not doing it right" that counts, which requires not to be vocalised.

To confirm this particular contraction is nonstandard, note just 3 instances of "I mustn't be doing" in Google Books, but 3830 for "I must not be doing" (almost all for the sense relevant here).

Both of your sentences mean the same thing. They are speaking on how you lament the moment you met the person.
If you wish to say that you never want to see the person again, consider, "I wish to never meet you again." This however would probably never be used in real life since it is extremely rude.