A technique for providing access to a data object serving as a target of snapshot-shipping replication includes taking a system snap of the data object after completion of each of multiple snapshot-shipping updates. In response to a data storage system receiving an IO (input/output) request to read and/or write to the data object, a data storage system redirects the IO request to a previously generated system snap, so that the data storage system performs the operation specified in the IO request on the system snap rather than of the data object itself.