I don't know what your back issues are so take this with a grain of salt. But in my experience, most throws don't require you to pick someone up to throw them; its more about leverage. I've been sitting here trying to think of any while I was typing. The closest I can think of is a step behind the back and a short stick to the front of the neck to a throw over the shoulder. Even then there is more leverage used bending the knees and hip to hip contact. But that is an advanced technique anyway. Note some of the answers about fitness, especially post #47. Those things may not work for you, but they may be worth a try.