Bespoke email alerts for private group

i would like to use private groups as a place where we can post public/anon URLs for others to gain access to online docs in Office 365. This would work fine except the URL is sent in the email alert, which is the thing we are specifically trying to avoid. is there a way to use bespoke email alerts for a certain category of group so that the person is alerted to an update without the actual update contents being in the email?