What in the world makes you think there is one? The very existence of a digital file with cut and pasted signatures and stamps argues against the idea that HDOH ever made a paper BC.
It is not a difficult stretch of the imagination to think they did both. I do recall reading that the White House showed some reporters a paper copy. Perhaps they printed it off the file themselves, or perhaps their claims of it being hand carried by their attorney are true. Either way, I think this proffered document was created by Hawaii DOH as a replacement for his original.
I personally think there is a good chance his original was an Affidavit of Home birth which was written and signed by his Grandmother. If you will recall, Fukino claimed to have seen it, and described it as "half-written, Half-typed." That description fits perfectly with what you would expect for an Affidavit of Home Birth, but not so much for a normal birth certificate.