I find blind grenades shots are a little unreliable. You can alternatively get Susie up to the sniper to use a hand grenade and have her take his spot, though you'll have to deal with reinforcements a little different if you do.
Have to say, that Mission Brief you get is absolute BS. If you hold, as you are told and then make a break for it with Edy, you'll end up with 5 Turns total and a "B" rank. Can't remember any other mission to have that crappy mission objectives without a turn reset.