I pray asr according to the hanafi time. Is it permissible for me to pray the shafi time if I know I will miss asr salah?
That depends on your beliefs. If you are convinced the Hanafi time is the only correct one, then the Shafi`i time will not work since it is much earlier. But if you study the matter and conclude that the Shafi`i time is correct, or if you ask a scholar you respect and they convince you the Shafi`i time is correct, then you can pray at either of those times without issue since the Hanafi time is later but still within the confines of the Shafi`i time.
But you want to limit yourself to the Hanafi school and wish to do everything their way, then you cannot use the Shafi`i time.