PizzaTijd

The "Mold" feature under 'Special Modes' might be of use here (it's hidden by default in the printer settings). It'll only print walls that are directly outside of your model - allowing you to literally use it as a mold for your model. Only difference is that instead of using it to cast a part, you'll be using it to cut dough.
 
The default thickness on my end was 5mm, which may be a tad much for a cookie cutter, but you can just tweak that and the wall angle to whatever you need it to be.

-Add a support blocker block
-Go to "Per model settings"
-Set it to "Modify settings for Overlaps"
-In the drop-down menu below it, set it to "Cutting Mesh"
-In the bottom left corner, while having your "support blocker" block still selected, select your second extruder
-Scale the "support blocker" to your required size, and set it to your required X/Y/Z
 
That should print everything in the area you marked with your 2nd extruder.
 
I call it a "support blocker" because it loses that functionality if you set it like this in the per-model settings.
 

In my experience it just makes sure that your print head is primed; that the material is all ready to go, as it has already extruded the skirt before moving over to the print.