All the "singer & laptop" outfits I've ever seen, have only ever had a single (maybe stereo) output from the laptop. After all, you should know how the mix should go, and it's just up to the soundman to EQ things.
Also, if this is your first gig, and someone else is doing sound, my guess is that you're either in a support slot, or in a quick change multi-act set up. In either case, setup and soundcheck time is going to be limited - you and the venue staff will curse an 8-line setup, and you're *much* less likely to get a good sound. But give them line & mic and you'll all end up smiling quicker!
I speak from experience as a regular gig-goer, and resident engineer in a 300 capacity venue.