To answer your question:
Most boards I plug into have RCA "tape" outs, so you'd need an RCA>stereo mini cable for that.
Some also have 1/4", which it sounds like you have covered.
A few have just XLR, for which you'd need an XLR>stereo mini cable or adapters for one of the ones you already have.
You will probably also need an attenuator, unless the sound engineer wants to be nice and be sure to turn the outputs down for you.
The bigger question is whether you really want just a straight SBD if you are only running 2-channel. How big is the room? If it's a stadium or a very large arena, maybe the house mix will be OK. If it's a club (call it 1500 or less), more likely than not the board will be poorly balanced with too much vocals/drums/keys and not enough guitars. It's not because the house doesn't know what they are doing; it is because the mix you are getting is what will sound good coming out of a PA system along with the stage guitar amps.
When mixed with an AUD source, a board is a great thing to have, but on their own, they can be pretty iffy. More likely than not, you'll get something that at best doesn't sound "right" and at worst is just a distorted mess because the signal coming in was too hot.
If you're married to the idea of running SBD, though, I hope someone can point you to a good attenuator cable. I don't own any myself as my deck can control hot incoming signals, but you will (almost) definitely need one.