This is exactly my situation (cooktop in an island with nothing above it). Our solution (because we cook a lot and often it's Chinese food with the attendant oil) was to just stick an existing rolling island in the garage with an induction hotplate on it and do our messiest cooking out there. Not ideal but it keeps the house cleaner and we didn't have to spend much.

Personally I would prefer a Chinese style kitchen with a fully enclosed cooking space (sliding glass doors to leave open if desired) and exterior ventilation. It keeps the worst of the aerosolized oil contained and away from the rest of the home.