Edit: I misinterpreted the parent; see below.

If by 'shuffle' you mean like Fisher-Yates, this can't work all the time, since that can produce, e.g. 0, 1, 2, 3, 4, 5 -> 1, 0, 4, 5, 3, which has two cycles. If by 'shuffle' you mean like Fisher-Yates, but not leaving an element in its original position, (i.e., generating a derangement) then this doesn't suffice either, since notice that the same example satisfies that condition and yet still has two cycles. You need Sattolo's algorithm (or something like it) to guarantee a single cycle.