My impression from a quick Google Books search is that the term nonreaders has often been used in recent years as a neutral way to identify persons who cannot read.
From Ronald Farrar, Mass Communication: An Introduction to the Field (1995) [snippet not visible in box]:
Catch phrases often used by nonreaders include: "I forgot my glasses." "I can't read that print." "I'll read it when I get home." "You read it for me." "I can't understand those big words." In questioning persons
From Sam Weintraub, Annual Summary of Investigations Relating to Reading, July 1, 1995 to June 30, 1996 (1997) [combined snippets]:
Using the results of the word identification test, the subjects were divided into 2 groups: 76 nonreaders, who could not identify any words, and 20 novice readers, who could identify 1 or more words. Anova and ancova procedures were applied to explore differences between nonreaders and novice readers on the various indices of phonological sensitivity.
From Judy Richardson & Raymond Fagan, Reading to Learn in the Content Areas, volume 1 (2003):
What can the content-area teacher do with the student who can barely read or who is a nonreader? The teacher can (1) pretend such a student is really not that bad a reader and do nothing, (2) get help from a reading specialist, or (3) assign extra work to help a student in this situation. Ideally, content area teachers do both (2) and (3).
Unfortunately for people who like to use language unambiguously, the term nonreaders is also sometimes used to identify people who simply don't choose to read a particular periodical or form of content (as in "nonreaders of newspapers") or to people who dislike reading despite knowing how. So illiterate is arguably a clearer term than nonreader for indicating the inability to read. But as discussed below, illiterate isn't an altogether unambiguous word either.
The point of euphemistic speech is to avoid using words that some hearers might find vulgar, offensive, or otherwise unpleasant—and it can hardly be denied that, in a society that prizes literacy, illiterate has negative connotations. Indeed, for hundreds of years, writers have often used it as part of extended insults, which is how pejorative senses of objectively neutral words gain their teeth. For example, from Samuel Low, The Politician Outwitted, a Comedy (1789):
HUMPHREY. A boar! why you're worser than he there—he only took father's corn for pigs, but do you take me for a boar, eigh? Do I look like a hog, as the saying is?
FRANKTON. Begone, you illiterate lubber!—My dear Charles, I have a thousand things to say to you, and this is an unfit place for conversation.
This instance is especially interesting because it illustrates the ambiguity of the word illiterate when used in a nonclinical sense. In fact, the Eleventh Collegiate Dictionary (2003) identifies several definitions of illiterate:
illiterate adj (15c) 1 : having little or no education; esp : unable to read or write {an illiterate population} 2 a : showing or marked by a lack of familiarity with language and literature {an illiterate magazine} b : violating approved patterns of speaking or writing 3 : showing or marked by a lack of acquaintance of a particular field of knowledge {musically illiterate}
Frankton's criticism of Humphrey in The Politician Outwitted might, therefore, be that he is generally uneducated, that he can't read or write (or both), that he doesn't show any taste for literature, or that he violates approved patterns of speaking.
From "Back Talk" in The Adjustor (September 1914):
That settles this phase of the financial situation pretty well, I should say, but out here on the coast we are principally interested in being informed why ... is the price of eggs being boosted to the neighborhood of 50 cents per dozen, and restaurant roast beef being sliced so thin that it is impossible to stick a fork into it? Answer me that, you illiterate, mouthing apology for a hiccoughing Washoe canary, and then go back to your manger and eat some more hay.
From Keith Peterson, The Trapdoor (1989) [snippet]:
Then the editor got the "message" signal on his screen and he pressed a button and the words, "[From Wells] You suck, you illiterate scum!" appeared right before him. Or something very much like.
Somehow, "You nonreader!" seems fangless in comparison to "You illiterate!" But if nonreader becomes sufficiently associated in the popular imagination with the underlying notion of illiteracy, it is likely to acquire pejorative connotations itself, and its usefulness as a euphemism will come to an end. At any rate, that seems to be what happened with retarded as a euphemism for "having unusually low mental capacity."