Is there a single word for a "unit of time"?

"Time unit" is correct here. "Duration" and similar terms refer to a slice of time (like two hours) not merely to the unit itself.

Of course you may be able to simply leave the box unmarked -- if someone sees "days" in a dropdown they'll know what it's there for.

Period, interval, or duration?

How about "duration"? I think that'll work for you…

Time-span, timespan, or time span, maybe?

Etymology for span:

span (n.1) "distance between two objects," O.E. span "distance between the thumb and little finger of an extended hand," probably related to M.Du. spannen "to join, fasten" (see span (n.2)). The Gmc. word was borrowed into M.L. as spannus, hence It. spanna, O.Fr. espanne, Fr. empan. As a measure of length, roughly nine inches. Meaning "length of time" first attested 1590s; that of "space between abutments of an arch, etc." is from 1725. Meaning "maximum lateral dimension of an aircraft" is first recorded 1909. Attention span is recorded from 1922. timespan (plural timespans) An interval of time.

So, what you're left with is a unit of time, to what measurement is left for guessing.

Or you could use unit of measurement, but again, this leaves quite a bit to the imagination of the reader - and who exactly going to be reading it? The user? Or other developers? Personally, I would choose what is going to be clearest to both, including to you in the future. If something represents a day, call it Day, similarly: Hour, Minute, and so on.