What are some non-surgical ways to deal with my spinal stenosis?  

Many little things. Doing things differently than you have been. Pain management can be helpful if it helps you move more normally. Breathing slow and deep helps. Fast and shallow is hyperventilating which aggravates your pain experience. Gentle osteopathic manipulation (no cracking stuff! ) can help increase body awareness and ease of movement. Learning to unclench your jaw will help you learn 2 relax overall.
Several. Activity modification, use of a 0 degree lordosis back brace, use of a cane or walker, medications, exercises/physical therapy as well as epidural steroid injections are all non surgical treatment options.