I asked my hubby and he wasn't sure either. He is thinking that you should use a caulking close to your color of wood on the lip underneath the stairnose. After placing the board on the flat step, put the stairnose (with the caulking on it) down and wipe off any excess that has squeezed out. The reason he says to do that is so that if you were sweeping off your stairs, it wouldn't collect in the gap and leave a bunch of crap there. I would put a thin line of caulking on the lip. Enough to close the gap, but not too much that you spend a ton of time on the clean up. I wouldn't want to see the caulking either, but he thinks if you put it thin enough and it matches the wood color, you won't have as much of a problem as that gap.

Hope it helps! Probably not as you don't want the caulking.