Do I really have to cut my wood flooring to a 1 inch width?
At this point, the answer is yes. You can plan to avoid this kind of thing in the design phase by ripping down the first row, but if you're already 99% done with the install, it's a bit late for that.

One final, if not ideal option is to have a really wide baseboard and add shoe molding to the bottom, which could conceivably cover up that kind of gap, but you'd have to commit to doing this on all the walls or else it will look funny.