Disinterested and uninterested do not mean the same thing; in this context, you want the latter.
Begin a new paragraph whenever the speaker/person acting changes.
Paperwork is one word, not two.
When only two characters are speaking, it’s neither necessary nor desirable to use attributions for every line of dialogue.
Although it’s possible to sigh while speaking, and sighing does affect the sound of the speaker’s voice, it makes more sense to limit sigh as a speech verb for short sentences (the sort that can be easily spoken on one breath). In the example, the sigh works fine… as separate from speaking.
As you make your way through a checkpoint on the space station, you stop at a booth manned by a bored alien.
Not looking up from its paperwork, it asks uninterestedly, “Name?”
You reply in the same tone. “Legal or preferred?”
You sigh. “Experiment J35-59DKO-B.”