The shortest variant would be using the temporal preposition in instead of an, as you already found out. In this usage in already implies that something happens within the time span further specified. It should therefore be clear that a single day only is needed.
Ich kann das Buch in einem Tag lesen.
I can read that Book within a day
There is some ambiguity with in as it can also mean after a day, however context should make that clear, and most people would then say erst in einem Tag.
This is also a good use case for the tiny but powerful adverb nur if we want to further stress the fact that is was only just a single day.
Ich kann das Buch in nur einem Tag lesen.
I can read that book in just one day.