No, no, no. The correct way to pronounce Malheur County, when you're in Malheur County, is the way the locals do. (Supposedly, the name of the county came from the Malheur River, which was supposedly named "Rivière au Malheur" by some French trappers whose property was stolen from their camp along the river in the distant past, at least according to the Oregon Blue Book.)
That applies everywhere. For example, if you're standing on Bowdoin St. in North Portland, there's only one "right" way to pronounce the street name. Good luck, if you're not from around there.