Keep the sustain pedal down. To see what the rest is for, do this experiment. Play just the right hand, without pedal. First play those notes as a dotted eighth and a sixteenth. Then play them as an eighth and a sixteenth rest followed by a sixteenth. You should feel a different character to the sixteenth, even apart from the rest itself. Now do it again with the pedal down. Even with the pedal down the sixteenth will keep its different character. That character, I think, is what Chopin was aiming for, and the pedal does not prevent it from happening.