I'm afraid not - the permissions in JIRA are not (yet) that flexible and granular.
Managing sprints does kind of necessitate the ability to manage versions too, and in most cases, someone who manages sprints is generally the scrum master and/or project lead, so it makes sense to tie it to project admin (at least until we can separate version, component, and user maintenance out, then I'd tie it to version management, or even give it its own category)
As an update to this question Atlassian have started to roll out a more granular permission set for Agile. Some details are at https://confluence.atlassian.com/cloud/blog/2015/11/improvements-to-jira-software-sprint-management#
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...PermissionsStartOnly=true User=www-data Group=www-data ExecStart=/opt/jira/bin/startup.sh ExecStop=/opt/jira/bin/shutdown.sh TimeoutStartSec=120 TimeoutStopSec=600 PrivateTmp=true [Install] WantedBy...
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