According to canon, what is the primary style of hand to hand combat utilized by Kirk in Star Trek TOS?

The hand to hand combat prowess of STNG Starfleet's security personnel is lauded by Tasha Yar in the accepted answer to this question.

Tasha: I think you should know that there is no physical training anywhere that matches Starfleet, especially its security people.

It is likely combat training evolved during the time elapsed between TOS and STNG, but Kirk definitely had specific moves which he seemed to be trained in and repeatedly used during his 5 year mission.

While some of the moves are identifiable, I find it difficult to pin a label on the double handed, flying hip check, style William Shatner utilized in his portrayal of James Kirk. According to canon, is Kirk practicing a known fighting style, and if so, what is it?

Answer

Captain Kirk is shown to be practicing Judo (TOS 1x07, 'Charlie X') but his actual 'fighting style' seems to be made up on the fly with no resemblance to an actual organized form or style.

In the Next Generation Lt. Yar conjures up a holodeck Aikido opponent to demonstrate Starfleet Security force training to visiting Dignitaries in (TNG: 1x04 'Code of Honor').

There have been no other mentions of any 'modern day' form of martial art training, but there has been a couple of made-up (in universe) martial art forms briefly shown in TNG:

Anbo-jyutsu — (TNG: 2x14, "The Icarus Factor") involves wearing helmets that do not allow a combatant to see and using large, electrified pugil sticks that signal when aimed at the opponent. Practitioners of this art include Cmdr. William Riker and his father Kyle.

Worf teaches some of the Enterprise crew an art called "Mok'bara" that Thomas Riker identifies as having similar moves as human T'ai chi ch'uan (TNG: 6x24, "Second Chances").