Work Permit with driving misdemeanor

I can't see it being an issue. Unless, of course, you were driving a car full of stolen kids. Then that's a different matter.

I think they will just sh!tcan u and choose the next applicant

I can't think what kind of driving offense would show up as a criminal violation except a DUI or an accident involving liquor.    It sounds like nobody is responding by saying that they had the same and got a work permit.  I guess the only thing you can do is try it and see what happens.   It might sound unkind but if you could a) detail exactly what the violation was and b) report back either way what happens, it could be instructive.

Of course in the unlikely event that you had the funds to live without working for six months, you could use a Vietnamese criminal check.