Persian migrated into Siam in the late 16th cent. and their history are well documented. We can trace back up to an Iranian named "Chek-Ahmad" (Sheikh Ahmed, I guessed) and his younger brother who visit Ayuthaya as merchants. They decided to settle down in Siam and do a lot of business with persian side. Later, many persian migrated into Siam and form persian colonies. Today, some of them still exist.
Chek-Ahmad is also the root of "Boon-Nak", a noble family, who served the royal family for centuries. The merchant brothers were very welcome by Siamese. After Chek-Ahmad and his men strenghten royal and city guard, solved a rebeling problem and then he was promoted to a very high-range noblehood. Beside his merchant business, he introduced islam (Shi'a) to Siam and also provided hourse and calvary trainig to the Siamese military.
Back to the topic, I don't feel persian battle axe is standard weapon for persian-adopted Siamese soldier. Persian-adopted units are mostly calvary and they served as bracers in the field. Accoeding to the national museum of Thailand, standard calvary weapons are agile polearm such as "Tuan" (lance) and "Tomorn" (trident) not axe or such.
