If I was in your shoes and the Airwave install currently isn't highly used or critical, I would go ahead and download the 7.7.10 ISO or OVA image from the support site and reinstall the application.
If you wish to attempt an upgrade, the rule of thumb is you can skip one major revision on an upgrade.
So at 7.3, I would upgrade to 7.5...then to 7.7.x.
However, CentOS was also upgrade which may have special considerations in your install. Might be worth a support case or a good read of the install/release notes.