Good morning David
I've had the same issue after completing a portrait especially one with a lot of fret work as to how do you apply a finish. Here's what I've done that satisfies my taste:
Prior to adhering the pattern to the wood I sand the surface lightly using carbon 1600 grit paper, wipe clean with distilled water. Then I use a cabinet makers wax applied with a clean cloth rubbing in with the 1600 grit paper and finally polishing with a clean cloth. I'll apply this process to each stacked item I'm cutting except the top one that the pattern is adhered to. I then place a plain sheet of white paper between each prior to taping which seems to help to eleviate any heat from the blade affecting the finish along the cut edges. After the portrait is completed I vacum leaving me with a natural finished item. I'm not sure how ths process will work using other types of finishes applied, but this is what works for me being I like a natural finish, so I'm not sure if I've been of any help or not.