How is that ironic? Saying "risk is our business" doesn't imply you'll be successful. It implies the risk is worth it, and you acknowledge the possibility of negative and dangerous outcomes.

no, because risk and danger is an expected outcome of what he said.

a weak situational irony would be that the crew reluctantly agrees to take on the risks of exploration, but then every single encounter they have from then on is peaceful, contemplative, and non-eventful.

a weak character irony could be that Kirk gets the crew on-board with his gung-ho antics and thirst for the unknown, they all agree -- and then it's discovered that Kirk is actually a huge wimp that was really just putting on a front because he never thought the crew would want to continue after his descriptions of danger.