Granted that takes the action into more interesting discussion areas because we can argue Kirk did not (and could not obtain all the information in time) before a decision had to be made.
Risk the Narada passing through in some fashion that didn't fully destroy or incapacitate it and just sit by and watch as it happens...............or take the decision to ensure it cannot do so definitively. Given how dangerous and capable Nero already proved to be. You simply can't take the chance. He was offered help and he pointedly refused it. Fine.
However, there is no proof any innocent prisoners (although it has been a few months since I watched it) were on that ship so the suggestion he killed innocents is not proven. It can't be proven or disproven based on the film either but even if there were for talking sake then clearly trying to save them would have been (assuming you had the time and ability to find and separate out innocent prisoners from the crew of the Narada) something that jeopardised the Enterprise very quickly thanks to the Black Hole itself. As Martok points out more humourously......'maybe' there were innocents aboard the Death Star. Doesn't mean there was time to save them before the thing had to be destroyed first for the safety of others.
But it does raise the question of what we would do or try to do in Kirk's position.
'If the Apocalypse starts, beep me!' - Buffy Summers
'The sky's the limit.....' Jean-Luc Picard, 'All Good Things'
courtesy of Saquist