It's not clear whether you mean I am being pedantic or you are, but it
is clear to me at least that you are trying to be even more so.
I do have virtually native competence in Japanese, you know.
I can't see for the life of me what Hiragana, Kanjii, or Katakana have to do with it. Rakugo, like any Japanese word, can be written in any of them, though for every Japanese word one of the three is the correct conventional orthography, being the most appropriate on the basis of its etymology and morphology and/or semantics. In the case of Rakugo that one of the three is Kanji.
You too are correct in that Rakugo involves a memorized script, but the 'style of stand-up comedy' is as I said before, a sit-down style of stand-up comedy. Rakugo is never delivered standing up, but only in the formal Japanese 'seiza' sitting posture, which you may know from Zazen (in both words za is a Kanji meaning 'sit') or the Tea Ceremony.
But you are not correct in calling the 'Rakugoka' an "actor", even in inverted commas. No properly informed Japanese would ever agree that he was any sort of "actor". No Japanese word translatable as 'actor' could possibly be used of a Rakugoka, tho some do moonlight as actors.
Similarly no Japanese word translatable as 'play' could possibly be used of Rakugo, and that is because it by no means "resembles a one man play in our Western context". It is a highly elaborate anecdotal comic monologue, and an acceptable expression for your "actor" would be 'comic story teller'.
That was off the top of my head. Wikipedia is better:
http://en.wikipedia.org/wiki/Rakugo