Bridget - from Corvallis, OR
You don't indicate what kind of icing or candy you are piping the monograms with, but parchment paper will peel away from hardened Candy Melts and royal icing with no issues as long as your monogrammed letters are not extremely thin. If they are very thin, make extras and plan for breakage.
I would suggest cutting out a small circle from fondant or gum paste and piping the monogram onto that. The circle will provide much-needed support, and once your monogram dries, you can store them in a cool, dry area between sheets of parchment paper. Prop it up on the mini cake by piping a small rosette of icing behind it.