Externalities arise out of incomplete property rights. The only externalities that arise from an airport expansion proposed in Wellington is from noise.
There are no externalities from building sports stadiums or hosting mega sports events because all of the effects are transacted through the market. No inputs are used without the permission of the owner, nothing is produced that is not charged for by the venue or event organisers.
As for the use of benefit cost analysis to strengthen the claim for a government subsidy, you use cost benefit analysis when you are too stupid to charge for the good or service such as a road or you are evaluating regulations because they deal with nonmarket effects, effects that are not mediated through the market process.
Sports stadiums and mega sports events should pass the usual market test. Is it profitable for the entrepreneurs backing the project when they are using their own money.