Times for accumulation of chemically significant dosages on icy surfaces of Centaur, Kuiper Belt, and Oort Cloud objects from plasma and energetic ions depend on irradiation position within or outside the heliosphere. Principal irradiation components include solar wind plasma ions, pickup ions from solar UV ionization of interstellar neutral gas, energetic ions accelerated by solar and interplanetary shocks, including the putative solar wind termination shock, and galactic cosmic ray ions from the Local Interstellar Medium (LISM). We present model flux spectra derived from spacecraft data and models for eV to GeV protons at 40 AU, a termination shock position at 85 AU, and in the LISM. Times in years to accumulate dosages ~100 eV per molecule are computed from the spectra as functions of sensible surface depth less than one centimeter at unit density. The collisional resurfacing model of Luu and Jewitt is reconsidered in the context of depth-dependent dosage rates from plasma, suprathermal, and higher energy protons, and global exposure, by micrometeoroid dust grain impacts, of moderately irradiated red material below a thin crust of heavily irradiated neutral material. This material should be more visible on dynamically `cold' objects in the ~40 AU region.