A ventless hood? Been there, done that. If you cook at all you'll regret this in the long term. Find the dough-re-me somewhere, install a vent and vented hood. I'm partial to the Broan Allure III, FWIW.
You may be able to draw power from one of the outlets depending on what else is on the circuit. Or you may need to run a new line tapping into another circuit or from the panel. Ask your electrician. In either case there will likely be some minor sheetrock damage needing repair. Since you haven't installed cabinets yet and it sounds like you haven't painted yet either, the repairs are no big deal.