Okay, I'll take a shot.
Your birth date does not correspond to Fixed Fire. You don't determine that from the Court Cards; you determine that from the Sign itself. Anything else is a misapplication. So, again, you're not Fixed fire. If you're Cancer, then your corresponding elemental quality is Cardinal Water. Don't let that confuse you any longer. You are correct that your birthday does not fall under the Sign of Leo, which is Fixed Fire.
However, the Court Cards do break down differently than the Signs. It's only used that way if you're meditating, selecting a Significator for a reading, or if you're trying to determine a window for the birthdate of a person (Court Card) that shows up in a reading. But it doesn't have anything to do with determining the elemental quality of the Sign under which a person was born.
So, yes, your late Cancer birthday makes you a Cancer Sun-Sign (which is Cardinal Water). But if you're looking to represent yourself in a reading according to your birthdate, then you are the Prince of Wands, which, yes, is made primarily up of Leo decans with one Cancer decan. But that doesn't mean "you're Fixed Fire." It doesn't have anything to do with that. That is determined by the actual Sign alone.
For an explanation of why the decans are separated like this, please see Liber Theta, p. 62, para. 4 & 5.