This is something your analysts can do though it requires a permissions change if they're not able to do it now.
The things you'll want to consider are, do they want to do this on a system dashboard or a personal dashboard?
I typically setup permissions to allow them to do this on a personal dashboard but not a system dashboard. System dashboard changes are kept as personalization and what that means is the user will always see their personalized version of that dashboard regardless of any changes you make as the system administrator.
So when I set this up I normally do it so they can only make these changes on a personal dashboard because administration will become a nightmare if each user has a personalized version of a system dashboard. You'll need to make a system dashboard change at some point and your changes will never show for those users with personalizations.
Hope that helps. Let me know if you need a listing of those perms.