Can I bypass power steering cooler on a 2003 chevy trailblazer

You can. I've done it on some cars but I live in a 4 season area. If you live or drive your car in a hot climate or drive it hard you may experience the fluid bubbling out of the reservoir. Synthetic oil may help too. If you don't work on your own cars then use this link to find a good shop near you. https://repairpal.com/repair-shops Alex