Many religions claim to be the only true religion, including most
branches of Christianity. Among the major Christian traditions, are
there any documented statements of faith that include the possibility
that their own beliefs might not be the "one true religion"? In other
words, is there any literature treating religious doubt accepted in
the tradition as part of the tradition, and not examples of individual
cases of religious doubt?
I think what is important to clarify is the difference between these two sentences above, which I will highlight by proposing two statements below:
"We, as a faith community, include doubting we are correct in our belief as an official part of our belief, and so we announce these doubts in [doubt literature x]."
"We, as a faith community, understand that doubt is a normal human experience and that our adherents will likely, on occasion, doubt some or all of the tenets of our faith, and so we address this experience in [doubt literature x]."
I am not aware of any "major Christian tradition" that has an accepted literature of the first type; that kind of institutionalized doubt is really not the purview of any religion, but is perhaps more the territory of scientists and skeptics. It is unlikely religions would succeed as social phenomena if they made it clear in their official PR that "hey, we could be wrong on all this."* And in this I agree with Steve's answer below.
(*Though, humans being as strange as they are, it would be fascinating to be shown that I am wrong and that there are such traditions and statements.)
At best, some Christians may acknowledge that, while they are not wrong, other religions are "as correct as they are" in that they are all paths to the same union with the divine. I think Fr. Thomas Keating, for one, may be amenable to this, though he is not representative of the entirety of Catholicism by any means.
As regards statement (2), though: In the Catholic tradition, there is something of a literature in this regards, yes. The Catechism of the Catholic Church, for example, allows some leeway for a distinction they make between voluntary doubt and involuntary doubt:
Voluntary doubt about the faith disregards or refuses to hold as true
what God has revealed and the Church proposes for belief. Involuntary
doubt refers to hesitation in believing, difficulty in overcoming
objections connected with the faith, or also anxiety aroused by its
obscurity. If deliberately cultivated, doubt can lead to spiritual
blindness. (CCC 2088)
Also, within the Catholic tradition there is also treatment of periods of spiritual torpor or feeling a lack of God's presence--sometimes referred to as "spiritual dryness" or also "acedia", and that may include doubts. One often refers to St. John of the Cross's poem, The Dark Night of the Soul as a Catholic touchstone on this issue and that title has come to refer to the phenomenon itself. In addition to St. John of the Cross, notable Catholic figures like Saint Thérèse of Lisieux, and Mother Theresa of Calcutta, who, it was found, claimed to have suffered from it for just over 50 years.
If there is such literature, and if this point is covered within it,
how do these major traditions view themselves in light of the "risk"
involved if they were wrong in the claim to exclusive truth?
I am not aware of much in this regard, other than perhaps Pascal's Wager, which has been incorporated into the literature of various Christian apologists, in which he argues that the "risk" is something like finite inconvenience (as compared to the risk of infinite suffering).
Again, as Steve essentially pointed out, trying to promote religion by calling attention to the "what if we're wrong?" issue is sort of like trying to sell used cars by pointing out the puddles of transmission fluid all over the lot.