Cook steak in oven with tray meant for deserts?
To answer your question directly, if the method of cooking is what I think it is, the pan you use should be fine, even if it has a nonstick coating on it. You can read the second section to see if my assumption about your cooking method is correct.

It's important that you don't use nonstick cookware for extremely high heat cooking. If the nonstick coating gets to the smoking point, it releases gases that are toxic enough (as a friend tragically learned) to kill pets. This includes pans that go in the oven, and on the stovetop.

Since the temperature at which you're cooking the steak isn't that much hotter than you'd use baking cookies, it should be fine. If it does have a nonstick coating, you should not use it under a broiler, which is much hotter than just sitting in the oven while it bakes.



Even though it's not exactly what you asked, since you don't seem to be super confident in what you're doing, I'll give you a little more info on what I believe is the technique you're trying to pull off.

I think what you're referring to is the method of cooking where you cook a steak slowly in the oven until the internal doneness (rare, medium rare, etc.) is just how you like it, and then you give it a good hot sear in a pan so you form a flavorful crust on the outside. It's pretty intuitive when you consider the following:


Making sure steak (or chicken, or pork chops, or other quick-cooking cuts of meat) is cooked through simply involves getting it to the desired internal temperature. The more consistent the internal temperature throughout the meat, the more consistent the texture and juiciness. 


The best way to control the overall internal temperature of the meat is to use gentler lower temperature methods of cooking so the inside has time to warm up before the outside gets overcooked.

Getting optimum flavor in a steak requires a nice sear/crust on the meat. 


The best way to get a nice crust on your steak is to add a decent amount of salt, and use a high-heat cooking method to trigger the Maillard reaction (what's happening chemically when browning occurs) and perhaps some charring.



You can see where the conflict lies between these two needs.

Using the method you read about, you can use the oven to gently bring it up to temperature so it's consistently cooked inside, and then you can use a pan (which does not have a nonstick coating) to give it a nice hot sear after it comes out of the oven. 

It is easy to overcook steak if you're not particularly experienced, especially using more complicated dual-cook methods. Nobody wants to eat a tough, dry mess. Though it's tempting to rely on cooking times you find on the internet, time is usually the least precise method to determine how cooked something is. I highly recommend using an instant-read thermometer to check the actual temperature inside.