The sunk cost fallacy is about continuing to incur additional sunk costs. The parent is arguing that we're going to have to pay $X/year to manage the nuclear waste we've already incurred and that the cost is fixed--adding more nuclear waste isn't going to increase the cost. Whether those claims are true may be up for debate, but it's certainly not a sunk cost fallacy.

He's arguing (to paraphrase) "Because we've already incurred such costs we should continue or even expand the policy which caused them."

Claiming that hazardous nuclear waste represents a fixed cost no matter how much you generate is simply absurd.

Do you have any data that says the cost (ie. money or security) is materially increased from this point forward given the space to store is truly small.

No, because the US currently has no such long term storage facility in operation.