Let's start with your last question.
I guess the easy solution would be just using dative, but I wish to know how a native speaker would write/speak.
A native speaker would use dative, at least most of the time. It depends a little on the preposition. E.g you might read sometimes (even more seldomly hear) dank seiner, but even here the more frequently used option (IMHO) would be dank ihm.
It is not so easy to find a general reference for this. On Deutsche Grammatik 2.0 the author writes
Bei Präpositionen, die standardsprachlich mit Genitiv und umgangssprachlich mit Dativ gebraucht werden, steht das Personalpronomen immer im Dativ.
The site, however, seems to be the work of a single author (a teacher for German as a foreign language). So it is not an official reference, and the rule has the additional problem that you need to know which prepositions are used with dative in colloquial speech. At least wegen is among them, for sure.
Then there is something on canoo.net. There you have an exhaustive list of prepositions that are used with genitive, together with usage examples and some general rules. Unfortunately they do not cover the case of pronouns, but from the examples you see that there are other cases, too, where dative is used instead of genitive, and I think these are examples where one would also rather use a dative than a genitive pronoun. Beside, many of these prepositons cannot be used with persons at all, so there is no question about personal pronouns for them.
Then to your next question
Are there irregular forms for the other prepositions, like for wegen?
Yes, there are. You have
- (um) seinetwillen
and the corresponding forms with meinet-, deinet-, unsret-, euret- and ihret-.
Is it bad style?
Well, to a certain degree style is also a matter of taste and opinion. I would definitely avoid it. It makes the reader or listener stumble at a point where I don't want it. For a second point of view, I recommend reading Wegen: Genitiv oder Dativ? at the blog Belles Lettres. There they strongly argue for using the dative with wegen, and I think some of their arguments could be applied to other prepositions, too. They even say
Präpositionen regieren im Deutschen und im Indogermanischen generell nicht den Genitiv. Man findet ihn nur bei Adverbien, die wie Präpositionen gebraucht werden.
But that would be the start of a new question...