Well first off buddy, I say: WELCOME BACK!!!!
Now, to your question,... You are 100% correct that due to the nature of things, Starship Captains do have 'a hellavu lot of authority in their scope of powers' - being judge, jury, and executioner - IN SITUATIONS WHEN COMMUNICATIONS WITH HIGHER COMMAND ARE CUT-OFF, OR THE TIMELINESS OF A RESPONSE WOULD PROVE ENDANGERING TO THE CREW AND ITS MISSION.
However, this is simply not the case in 'Space Seed'.
Therefore, based on that fact alone, I say, KIRK not only had NO AUTHORITY, but moreover usurped the UFC:SFC, the Chain-of-Command, and knowingly and purposefully violated his orders to deliver Kahn to the authorities for proper disposition.
And should be facing a COURT-MARTIAL himself!
So to answer your ACTUAL QUESTION in short: Breaking the very laws you are sworn to uphold, to enforce your own personal idea of what is 'just, humane. or right'; is rarely 'The right thing to do',.. The UFC:SFC has in place, procedures of petition AFTER the Captains' duty have been discharged,... and the criminal delivered to authorities.