The designer should do that for you. They haven't tested the templates in both Outlook and Gmail, and that (IMO) is part of their job. It may be too late for this time, but you need to tell them up front that these are HTML templates for email, and one of the requirements is that it work in Outlook.
Designers hate Outlook for this reason, but sadly, that's just how it is. We just have to live with it until Microsoft move into the 20th (never mind the 21st) century.