I don't remember Peter Pan specifically, but it would seem rather odd that Hook does not own a flintlock before he goes to Neverland initially. Flintlocks have been around since atleast the 16th century (in the LWM anyway), and cannons even before that. I'm pretty sure the Jolly Roger was equipped with cannons, and it would make sense that a pirate captain would have a flintlock pistol. Also, since JM Barrie fashioned Hook after many of the pirates that sailed the Spanish Main, a flintlock pistol would have been standard fair for the captain.
As for Hook not recognizing the gun in 2.11, That may have been more of not recognizing a modern pistol with it's more modern sophistication. The fact that he determined the purpose if it extremely quickly indicates (to me anyway) that he knew what guns were in general.
As I wrote this, I went and found a copy of PP on the internet and checked, and while it did not find HIM carrying a pistol, there was mention of one of his men (Starkey) holding a pistol. So, I would say that Hook knew exactly what a pistol was.
As a side note, in the original tale, it was Hook's right hand that was cut off, not his left (although most modern interpretations of PP have Captain Jas. Hook with his Left Hand removed).