There is a bike path around most, if not all, of Kapiolani Park.  Here’s a map of the area.  http://hidot.hawaii.gov/highways/files/2013/02/BikeMapOahu-5c_HonoluluDetailWaikikiKahala.jpg 

As I recall, in some places the sidewalk is right next to the path, so if you were on the sidewalk, then it’s possible you could be cited.  If you’d like to contact me with more details, I’d be happy to try to help you figure it out.