I agree with your method! Just be sure the jar is plastic, not glass!
Start shaking fairly gently, and as soon as you have 2/3rds or 3/4 as many seeds as you want, pour those out into a separate bowl or cup before you continue shaking. They are probably clean enough "as is".
Continued and harder shaking will make lots more small chaff as it releases a few more seeds, so spare yourself any cleaning of the first 2/3 or 3/4 of the seed.
I trade the cleanest seeds and plant the seeds-with-chaff. That's like mixing fine seeds with white sand: it lets you see where you have or have not sowed thickly enough.
