We examine the transfer of graphene grown by chemical vapor deposition (CVD) with polymer scaffolds of poly(methyl methacrylate) (PMMA), poly(lactic acid) (PLA), poly(phthalaldehyde) (PPA), and poly(bisphenol A carbonate) (PC). We find that optimally reactive PC scaffolds provide the cleanest graphene transfers without any annealing, after extensive comparison with optical microscopy, x-ray photoelectron spectroscopy, atomic force microscopy, and scanning tunneling microscopy. Comparatively, films transferred with PLA, PPA, PMMA PC, and PMMA have a two-fold higher roughness and a five-fold higher chemical doping. Using PC scaffolds, we demonstrate the clean transfer of CVD multilayer graphene, fluorinated graphene, and hexagonal boron nitride. Our annealing free, PC transfers enable the use of atomically-clean nanomaterials in biomolecule encapsulation and flexible electronic applications.