Squats and deadlifts are unequaled in terms of core strength development, and they are also some of the most natural human motions that any toddler naturally picks up as they learn to walk upright. I agree doing them with heavy weights can be risky for a typical sedentary adult, but they need not be feared. Performed correctly, the load goes into your muscles, not joints, but you have to learn how to engage your core muscles and maintain tension through the whole kinetic chain. The best way to do this is to get a knowledgeable coach and build up slowly starting with no weight until you have the basic movement and coordination well established.