Another option is to find someone on youtube who is playing the song (of course make sure it's a good enough quality of recording for you). Then just send them a message asking for permission to use their recording. Also, be sure to ask them if they wrote their own arrangement because if they are working off of sheet music a particular arrangement could be under copyright.
But, like the others have said, the melody and words for Silent Night are public domain, so you can always make a simple recording of it yourself.