Signature they may be, but it appears that dolphins' whistles aren't actually whistles. A true whistle relies on pushing air through a chamber, but a similar sound can be produced by a vibrating membrane.
To find out which way dolphins do it, Peter Madsen of Aarhus University in Denmark and colleagues recorded a bottlenose dolphin whistling after breathing helium. The sounds were largely the same whether the dolphin was breathing helium or air. If the dolphin was really whistling, the helium would have changed the frequency of the sound (Biology Letters, DOI: 10.1098/rsbl.2011.0701).
I am irresistibly reminded of this and this. (I could almost swear that I've seen a 19th-cent cartoon of a bloated, possibly airborne, Coleridge leaking out of his sides/rear, but I cannot find it anywhere.)