Some smith machines are weightless, some aren't. The ones at my gym I could lay on the flat bench and use my two pointer fingers and push the bar three feet above my body. Kinda like if I bench pressed on the moon. So I wouldn't add any weight because you don't know exactly how much it weighs. You'll be more accurate to not add any weight and just focus on progression with adding weight to the bar.
If you feel embarrased about any weights you're using, then sure, add in the weight. The point is to be as accurate as possible and focus more on progression, not how much.
BTW, where'd you get 22 lbs?