The number of changes between v9.4.3 (which is no longer under support by F5) and v11.4.x are massive.
If you want to keep your downtime to a minimum I would suggest a change freeze to allow you time to duplicate the configuration of your old box on the new one and then perform a hard cut. This would allow you to perform a quick back out if the upgrade does not go as planned to a known good device (what you are currently using).
The migration of the configuration from the old to the new is something that you will have to figure out since there are several ways to do it and it all depends on what you are comfortable with and allowed to do.
Good luck with your upgrade!