The blinds should cover the old holes I did something similar with a coat rack a few years ago, lots of holes looking for a stud, and just patched and painted as part of my most recent reno, probably nine years after making the holes. They were always covered up by coats so it didn't matter so much.

I still have one more piece of my project, refinishing my stairs. I started it a few weeks ago but ran into a problem when the product I was using did not work as expected (think bright pink blotches). I haven't worked up the enthusiasm to start again - it's just such a pita since I am not supposed to walk on them and it's the only way I can get upstairs. I guess I'll do every other like they suggested at the hardware store.