The wax used in wax paper is food grade paraffin wax, which is just a certain class of hydrocarbons that are nontoxic. Similar to what is used to wax fruits and vegetables. The fact that it is petroleum based isn't really important, because chemically, it's not a health hazard to people or to compost. The wax itself will not really break down very fast but since it is spread thin on the paper, it's not like putting a hunk of wax into the compost. I haven't tried it, I'm just speaking as an env. chemist and composter.
BTW any scrap candle wax at our house is saved up in a coffee can and melted down to make new candles. Some people offer it on Freecycle or Craigslist free section if they don't make candles themselves.
Both my wife and I have compost operations going at work. We use a gallon ice cream bucket with a handle and snap lid, next to the coffee stations. They're labeled "Used Coffee Grounds and Filters for Composting". The bucket goes home with you whenever you want, and replace it with a clean empty spare. Works quite well.