Does any such book exist in English? If not, what other major writings would you refer me to for understanding the theology of this communion?
There isn't much Pan-Oriental anything.
I take it you mean something "modern." For an Armenian one used in the Ottoman Empire:
Letters from Broosa, Asia Minor ...: with an essay on the prospects of the ... By Mrs. Eliza C (Abbott) Schneiderhttp://books.google.com/books?id=OBg3AAAAMAAJ&pg=PA96&dq=an+armenian+catechism&cd=1#v=onepage&q=an%20armenian%20catechism&f=false
An older one is contained in the Agathangelos Life of St. Gregory. It has also been translated seperately as
The teaching of Saint Gregory: an early Armenian catechism By Agatʻangeghos, Robert W. Thomsonhttp://books.google.com/books?id=TvrYAAAAMAAJ&dq=an+armenian+catechism&cd=2