For the first edition of the game I bought a metal miniature of either the Nakajima B5N "Kate" or the Nakajima B6N "Jill" (can't tell which one it is precisely) and painted it yellow. It stood out from the Orange plastic A&A pieces that we used for the Japanese. And it still fit on the carriers (unlike a bomber figurine- see below).
As John correctly states, they used just about anything that they could put into the air as a Kamikaze unit. Many of the original planes though were carrier aircraft that had been removed from the decoy sacrifice CV force during the Sho-Go attacks of the battle of Leyte Gulf when Kamikaze attacks were first employed. Later during the Okinawa battle, the force mixture of attacking Kamikazes was of a much greater diversity. Single and multi-engined, Army and Navy units, even the Ohka flying bomb.
I guess you could just as easily have picked a Aichi D3A "Val" or even a Mitsubishi A6M "Zeke". Or even a variety of obsolete early war land based fighters like the Nakajima Ki-27 or army bombers like the Mitsubishi Ki-21 and Ki-67 or the Nakajima Ki-49.
Also, as an aside- many discussion groups/boards don't use the term "Jap" (or "Nip") when referencing the Japanese. It is deemed a derogatory term on level with "nigger" when referring to blacks/African Americans or other terms like "spic", "dago", wap", "mick", etc.
What we use on the Empire of the Sun thread over on Consimworld is the abbreviation JP for Japanese or Japanese player.
It's really up to John or Mark as to whether it is a problem. Just putting it out there for discussion.