In October I purchased a M&P Sport through an on line retailer. The retailer has a clear policy that I could inspect the gun at my FFL and return the gun if there was any defect as long as I didn't "accept" the gun. The retailer would pay return shipping. I don't know how, but I missed a big scuff in the Melonite finish on the barrel and accepted the gun. My error for not taking the time to properly inspect.
So, I emailed S&W CS about a warranty claim. I received an auto response within an hour stating they had a high volume of emails and I would receive a response in 5 business days. CS was true to that promise. In 4 business days CS offered to send a prepaid shipping label. Once I responded to please send the label, I had a FedEx label in two business days. I sent the Sport in packaged according S&W's instructions via FedEx. You have to declare you are shipping a firearm to the manufacturer. FedEx gave me a tracking number and I tracked the Sport to FedEx.
About 3 weeks later I received an email from CS with the tracking number for the return shipment. I had FedEx hold the Sport at their local office instead of trying to catch the delivery driver. FedEx ( and S&W I presume) require an adult signature for delivery. I had no problems with CS or FedEx. Everyone was great. Ultimately I could have saved myself a lot of hassle if I had taken the time to properly inspect the gun. S&W replaced the entire upper and it actually fits better than the original scuffed upper. I finally shot it and it functions 100% and is one of the more accurate ARs I've shot.
At the same time my Sport was at S&W, I sent in the 686-1 I've had for 25 years for the firing pin bushing recall. S&W is still honoring the recall after 23 years. The turn around was quicker- 10 days from the day I shipped until my 686-1 was back. The Sport took 4 weeks overall. Work on the 686-1 was superb, plus they even tuned it a bit.
I've had S&Ws for 25 years and this was my first contact with CS. No complaints here.
I sent my two guns in to CS in October and early November. As others have said, with the holidays, holiday shipping, and the winter storms they are probably running behind. Since your Shield is new, use their warranty instead of possibly voiding it by working on it yourself.