That can work just fine. Shimano 8 speed spacing is just a 0.2mm smaller than 7 speed, so if the adjustment is dead on for gear 5, it will only be off a maximum of .6mm at gear 7, which is not enough to matter. I've used 7 speed shifters with 8 speed cogs and it worked.

You'll want to use gears 8-2 on the shifter if it isn't already.