Joe, See if you can link up with a Starwind user's group or another Starwind owner. They can tell you if the hull is cored. Then look at the threads here and elsewhere, manufacturers sites (eg. Hummingbird) to see their literature on the subject. You will find it a pretty simple matter to mount the transducer to get accurate and consistent readings.
On my Catalina 22, I've mounted the transducer 'puck' forward of the keel, placed in 'toilette-mounting' wax (some folks use epoxy). I first mounted a 3" piece of plumbing-PVC to the inside of the hull, sealing it in with marine grade sealant. I poured melted wax into the PVC fitting, pushed the puck down into the wax, covered the whole thing with a threaded access plug for the PVC fitting, running the transducer wire out through the top of the plug. Works like a charm and I didn't have to drill a 2" hole in the bottom of my boat.