A random shuffle is really a random selection from a uniform distribution of the set of all possible permutations on that range of numbers (or N!).
This assumes that you're chosing one member from the interval. However, even this has a gotcha or two. If you do this on a large scale, an attacker will surely notice that all of your "random" numbers come from the same interval and exploit this fact.
Moreover, in terms of randomness, a random shuffle and just choosing a random number are vastly different. One is chosing a member from an finite set without replacement, the other is chosing a member from an infinite set with replacement. That is to say that in the true random case, you are just as likely to pick the number that you just picked as you are any other number. In the random shuffle situation, you are guaranteed that this is not the case. An attacker can exploit this, too. For instance, let's say that the interval was [1,4]. As the attacker, you have this knowledge. Furthermore, you've observed, the following numbers go by: 2, 4, 1. What's the next number in the sequence?
And who said the numbers had to be used for cryptographic purposes?
Is there any other use? ;)
thor
Feel the white light, the light within
Be your own disciple, fan the sparks of will
For all of us waiting, your kingdom will come