Can you provide rights to a snapshot without providing rights to the database?
From Limitations and Requirements of Database Snapshots on TechNet:


  A database snapshot inherits the security constraints of its source database at the time of snapshot creation. Because snapshots are read-only, inherited permissions cannot be changed and permission changes made to the source will not be reflected in existing snapshots.


Update:

As Martin Smith suggested in a comment, one way is to grant permissions on database, take a snapshot, and then remove permissions. The login could be temporarily disabled for the period that rights were granted.