Any brand of cookware you are considering which states "non-stick" should immediately send a warning flag to you as it probably contains the very deadly PTFE. Unless the manufacturer can state in writing it does not and explain exactly how it is non-stick, assume it contains deadly PTFE. Some self-cleaning ovens, clothes dryers, hair dryers, space heaters, irons, ironing board covers, waffle irons, deep fryers, heat lamps and other small appliances or their components may be coated with non-stick surfaces. Unless the manufacturer verifies in writing that the product in question does not contain PTFE producing elements, assume it has them. Overheated, non-stick coatings emit odorless fumes containing PTFE which are lethal to birds and can kill within minutes. Whatever utensils you use, rooms should be well ventilated when cooking is in progress. Ventilate the bird's room or area as well as the kitchen. Fumes will travel within your home. Use a range hood, ventilated to the outdoors when you are cooking. Stainless steel or cast iron cookware is an easily cleaned alternative to pots and pans coated with non-stick surfaces.
Having personally witnessed the death of a friend's birds when she innocently used a new drip pan to broil some steaks in her oven, I can say it is a horrible tragedy to happen. Several budgies in a room off the kitchen with a door shut between all died as well as several cockatiels in an adjoining dining room. The only bird to survive was an amazon in a back bedroom with the door closed. He spent several days in the hospital but did survive the ordeal. Nothing can describe the horror the owner went through losing her beloved birds.