I'm no lawyer, so... with a grain o' salt...
My philosophy / understanding on all this was that our CCLI license gave us permission to use songs, but not to use someone else's performance or publication of the songs. So de-vocalizing the songs from a published CD is probably less than entirely legal. However, CCLI just came out with some new licensing stuff that apparently makes it legal to copy songs from published CDs to help the band learn the songs, so you might look at that to see if it says anything about using CDs like that in worship.
Aren't there a bunch of "split track" worship CDs out there? The songs are probably not the hot new numbers, but I would think that the publishers of those CDs would expect people to use those music tracks in live worship, maybe the copyright notice on those CDs even allows for certain uses like that.
We had a discussion on here not too long ago about using "Band In a Box" to create instrumental arrangements for songs; that would get around the whole issue of using someone else's "performance" of the song, and would also allow you to adjust song keys, tempos, arrangements... I'm several versions downrev on BIAB, my understanding is that the newer versions use lots of real instrument samples and the like, and they sound a lot better than "MIDI through a soundcard" stuff. With BIAB, you choose a style, tempo, and key and enter the chord pattern and it makes music for you... it's really simple to use and is probably noticeably more "legal" than stripping vocals from a published CD.
When you say "bring," are you referring to doing worship at your own church on Sundays when the drummer can't be there, or are you talking about going to other churches, public events, etc.? For what it's worth, I think the CCLI licensing does make a distinction there, as well... stuff you can do at your own church may not be covered if you take it on the road...
But like I said, I'm not a lawyer...
That thread also mentioned some software that
Audacity can't really do that that I've found. At least I've never been able to get a result that can be used for accompaniment. It really ends up sounding edited and is completely dependent on the design of the original. Maybe someone else has a different experience. That being said, you are still dealing with licensing issues.
When I run into "lack of musicians" I can always default to just me and my guitar. Are you an instrument player? I don't recall.
Do a google search for backing tracks, worship backing tracks, instrumental tracks, etc.
There are tons, they already have the vocals removed, some even let you select the order of the verses and chorus, or what instruments play.
Let us know more of what you are doing and perhaps we could recommend some websites.