Does the Airport Shuttle stop at Shenyang North Railway Station?

I'm afraid that no direct shuttle bus can take you there. I suggest you take shuttle bus line 3 to Ma Lu Wan. Then walk to the Maluwan bus stop to take bus no. 203 or 328 to the North Railway Station.

From North Railway Station, there is direct bus to reach. At the train station bus stop to take bus no. 105 or 168 North Line to get off at Xiaojinqiao Station or take bus no. 230 and get off at Dabeimen Station. Upon your getting off, you can easily walk to your hotel.
One more thing, it is within 5km between the two places, so you can also take a taxi to travel.