SAFETY should be your primary concern in all cooking methods. The danger inherent in cutting dense, hard, ROUND foods is that they tend to roll or shift when pressure is applied, thus allowing hand or fingers to suddenly slip under/against the cutting edge. One key to safety is STABILITY. Hasty chopping, hacking, swinging, or stabbing motions are dangerous--especially if you can't be sure the food will stay put. Firm, controlled movement upon a stable surface is the safe way.
Placing the squash on a nest fashioned from a tightly-wadded or rolled, clean kitchen towel is a good way to achieve stability. It is also important to work with a very sharp knife that has a rather thick blade. This acts like a wedge acts in wood-splitting. The knife should also be several inches longer than the diameter of the widest place on the squash, to allow for gripping both ends of the blade during the final cut through.
Place the squash on your towel nest, use another kitchen towel, folded, as a sort of mitt. This "mitt" should be thin enough that you can grasp firmly with it. (100% cotton towelling usually grips better.) Using your mitt, grip the wider end of the squash; insert the tip of the knife into one of the longitudinal ridges, with the cutting edge away from that mitted hand, until the knife has nearly come out the opposite side, lodging in the flesh of the squash on the opposite side. Then, lever the knife edge down in a motion that uses the lodged knife-point as a fulcrum. (Think of the motion of a paper-cutter.) Flip the squash over, repeating this, until the pointed end is cut all the way through. Up-end the squash, placing it on its stem end in the towel nest. Check for stability. Place your knife into the slit, perpendicular to the axis of the squash. Use your gripping towel to pad the non-cutting side of the knife, then press down until the squash is cleaved through.