Quilters have been cutting away the backing from behind hand appliqué for many years and I don't see any weakening in that particular area. It's usually done so that you don't have 3 or 4 layers of fabric in that one spot. When you trim you will be leaving at least a ¼" of the fabric your appliqué piece is made from so if it is light coloured the darker piece shouldn't show through, just make sure that when you trim you don't leave the darker one wider than the lighter one. If it's your first appliqué project maybe choose a nice rounded shape for your sample piece first.
Edited to add: if you prefer you can just cut a slit in the backing & pull the freezer paper off, you will need to use something like a tweezer to run between the paper & the appliqué shape to release the paper though. This is the method that I usually use.