Oversighters (and with those capabilities such as stewards and wmf staff) should be able to suppress newsletters or new newsletter issues. Please create a new right: newsletter-suppress with the capability of suppressing newsletters or individual newsletter issues, then have it assigned to oversighters.
As currently this is only on mediawiki.org and only administrators are able to use it the risk is low, but I consider this to be a blocker to further deployment to further Wikimedia sites until this is resolved. I expect some projects will also request new groups so non-admins be able to manage newsletters and we need to be sure that things can be suppressed in case things go wrong.