he acts disappointed when he doesn't die. he jumped with the intention to die.
no, he was disappointed that all he felt was a headache.
and when he said there's no choice but to go through with his plan, he meant his plan with joker regarding smiles and the war.
why would he choose to kill himself then when he's planning to start a war?
his dream is to create a massive world wide war and die like whitebeard or roger so that he is remembered for centuries to come. (unlike his captain).
everything else he does is a means to this.
smiles, ancient weapons, the alliance with big mom, one piece etc.
we see big mom, luffy openly claim that they wanna get to the one piece and become the king of the pirates.
but kaido has never once said that he wants to be the king of the pirates. all he wants is to die in a legendary manner for which people will remember him and finding the one piece and starting the great war that whitebeard prophesized is a means to that goal.