Can you approach the squeak with a few screws from underneath? Don't use drywall screws. They are brittle. Use flooring or deck screws. That would really be the best way assuming there is no carpet on top or the floor. You may have to cut some of the sheetrock ceiling below the floor (if there is sheetrock) just to avoid nail heads or screw heads from being seen. If the floor is carpeted there is a kit which has a break-away screw that is invisible under the carpet. I am certain others will come up with additional solutions. Squeaky floors are pretty common. Solutions depend upon where the squeak is arising from. Some old timers swear that putting talcum powder between the hardwood slats can aleviate a squeak. Again, depends why there is a squeak. Could even be wood rubbing against a nail as opposed to wood rubbing against wood. Every case is different. If you decide to come up from underneath the screw should be 1/4 inch shorter than the combined thickness of the subfloor and hardwood.