you can always use 'icky' fabric as stabilizer..
For example I have some super thin flimsy see thru fabric that i would not trust in a block, however I used my go circle die cutter.. layed right side (good fab) to right side (icky fab) and cut.. i sewed all the way around the edge- 1/4 inch... and slit a hole in the icky fabric and 'birthed' the circle.. Now i have a clean edge to applique..