Europa's icy surface is radiolytically modified by high-energy electrons and ions, and photolytically modified by solar ultraviolet photons. Observations from the Galileo Near Infrared Mapping Spectrometer, ground-based telescopes, the International Ultraviolet Explorer, and the Hubble Space Telescope, along with laboratory experiment results, indicate that the production of oxidants, such as H2O2, O2, CO2, and SO2, is a consequence of the surface radiolytic chemistry. Once created, some of the products may be entrained deeper into the ice shell through impact gardening or other resurfacing processes. The temperature and pressure environments of regions within the europan hydrosphere are expected to permit the formation of mixed clathrate compounds. The formation of carbon dioxide and sulfur dioxide clathrates has been examined in some detail. Here we add to this analysis by considering oxidants produced radiolytically on the surface of Europa. Our results indicate that the bulk ice shell could have a approximately 1.7-7.6% by number contamination of oxidants resulting from radiolysis at the surface. Oxidant-hosting clathrates would consequently make up approximately 12-53% of the ice shell by number relative to ice, if oxidants were entrained throughout. We examine, in brief, the consequences of such contamination on bulk ice shell thickness and find that clathrate formation could lead to substantially thinner ice shells on Europa than otherwise expected. Finally, we propose that double occupancy of clathrate cages by O2 molecules could serve as an explanation for the observation of condensed-phase O2 on Europa. Clathrate-sealed, gas-filled bubbles in the near surface ice could also provide an effective trapping mechanism, though they cannot explain the 5771 A (O2)2 absorption.