You can go ahead and start the dorian with the double chromatic approaches. You can always go back and do the previous calisthenics if you wish. However, the dorian just has the b3 instead of the maj 3 in comparison to the mixolydian, so you shouldn’t have that much trouble applying the previous approaches to it.
Eventually (with a few exceptions such as the super locrian), what you practice in terms of approaches over one scale will carry over to a new scale, especially when said scale only differs in 1 note. In the etudes, rhythm templates and candy bars, you will have the opportunity to use the new scale (in your case, the dorian) with all the previous approaches also.