The only way I think of is to disable Embed New Attachments, found under Settings - Email - Options.
It will then send all emails, with a link to WHD for each attachment, rather than sending the attachment within the email. They would need to login to view the attachment if required.
This will also affect all future emails, not just the new ticket email.
Hmmm, that would work for the group that needs it, but mess up the other groups... I know it's really specific, but anyone know of a way to set it for 1 group? I was looking in the templates, because they have their own, but I can't seem to set it not to do that.