Yes indeed. Using backing tracks transferred out as WAV tracks on whatever device you want to use for playback is the way to go.

I was, for a time, involved in a prison ministry. I actually used my small MP3/wave player to play the tracks. I'd take a few minutes and create a play list for that particular event. When I got there, I'd set up the small PA, plug in and I was ready to go. I also had my acoustic guitar and lyric sheets as needed. The main speaker would also use the PA, which was owned by the church sponsoring the ministry. We'd generally have 8 to 10 people from the church at each of the events.

In your case. you're doing it right. I would however, see if you can find someone who can sing to assist with leading the singing. You don't want to take just anybody.... get someone who fits. I understand that in a small church that may not always be possible.

You can find my music at:
www.herbhartley.com
Add nothing that adds nothing to the music.
You can make excuses or you can make progress but not both.

The magic you are looking for is in the work you are avoiding.