My grandmother 1883 - 1980 insisted that a "missive" was a HAND CARRIED message or letter. I don't find this distinction in modern thinking. Any ideas?
About the etymology, according to Etymonline:
(n.) mid-15c., "commandment," noun use of adjective (mid-15c.) meaning "sent by superior authority," from Medieval Latin missivus "for sending, sent," especially in littera missiva "letters sent," from Latin missus, past participle of mittere "to send" (see mission).
If we take a look at Collins:
1) a formal or official letter
2) a formal word for letter
So I would say that the first sense (formal letter) comes from littera missiva in the sense of 'letter sent by superior authority' and a letter sent by 'superior authority' would most likely be hand-carried). Afterwards it probably started to designate a 'common' letter.