Reset permalinks for all blogs?

Does anyone know if there is an easy way (or plugin) to mass reset the permalink settings for all existing blogs? I would like the setting change to be immediate, not reliant on a user logging into Site Admin.

We have a number of blogs that seem to have gone 404 on post links due to a nasty plugin and resaving permalink setting is the only way to fix. But, we disable the Permalinks option in settings for all users.

So, would like to do it for them.