Hi MG,
I'm unsure there is a verb for "doing archery", and suspect dody's shooting may be as close as we can get. After all, bows and arrows have been around for a heck of a lot longer than guns, and until guns arrived people wouldn't have had anything else to shoot with. This presupposes that "shoot" predates "gun" of course.

I suspect "cockup" for wrong position of fletching may be reatively modern

Hmmm, not convinced Bill. Many terms from archery are embedded in English from way back, and archery skills were hugely important to the English people. So I think it makes a lot of sense that "cock-up" should refer to an arrow that doesn't fly straight due to being knocked (? think that's the word) incorrectly.

This reminds me of the (supposed) origin of the English gesture flicking the V's (aka V-sign, two-fingered salute) amongst English archers during the Hundred Years War:
http://st.sebastians.org/Info/FAQs/Longbow.php

Some other interesting archery/longbow stuff on that page.

Fisk