Deleting an item from your Deleted Items folder doesn't immediately permanemently delete the email as there is a recovery period. You will also need to purge it from the recoverable items before it is permanently deleted. This shows you how to do this in Outlook 2016 and Nexus365 (Outlook365).
Advice from InfoSec about using email securely, sending documents by email and alternative solutions to sharing documents by email.
By mail merging email you can create individual emails for bulk recipients rather than sending the same email to all recipients.
Make sure you don't share information you weren't intending on spreadsheets.
If you regularly email documents to a group of your University colleagues consider using a Nexus365 Team instead.