That would be just like using mono delay config and reducing mix or input gain.If you use dual anyway, you can turn down "Level right" to zero and set "pan left" to middle or zero and then turn down "level left" to maybe under 50%, it will then be mono and a very low level delay.
There are more consistent ways than ducking to make delays decay faster from second repeat onward. For example, pan dry signal left into dual delay with equal L/R times, both delays panned center. Feedback L>R = decay from 1st to 2nd repeat; Feedback R>R = decay from 2nd repeat onward. Leave other feedback controls at 0.