Find 1 tuning that works for your singers voice and make that YOUR "standard" tuning for the band. That way you play everything in that range and don't have to keep re-tuning or switching guitars.
Like I mentioned, our band plays in drop tuning, but we do some covers that are in normal tuning (Eb standard tuning). So the only re-tuning we ever do is just bringing the low E string up or down a step.
The only problem I see is if you have a floyd rose/floating bridge setup. Can't just tune 1 string up and down because it will throw everything else off. Good thing I play bass for the band so I don't have to worry about any of that :cool: That's where having 2 instruments to switch between comes in handy. Have 1 in drop tuning and another in standard (whatever your bands standard is) and you should be good with anything.
As far as being a cover band though, I'm not too sure. I guess it depends how picky your crowd is. If they are going to be disappointed that you are playing in Eb and not Standard, then you have quite a picky audience.