So far it looks like oily Hakan has three main options on wakeup.
1. Focus attack dash normal cancel. This deals with meaty attacks that have lots of active hitting frames and/or have long ranges.
2. Backdash normal cancel. This deals with chained meaty attacks, throws, and some armor breakers.
3. Plain ol' backdash. Deals with most armor breakers, most meaties, and throws, but you don't usually get to deal much damage out of it.
Tinshi's video showing wakeup backdash normal canceling: • Video
Dias4Flac's video, the first one on YT to show unthrowable toward+rh: • Hakan's Auto Tech Grab (Forward Hard Kick)