Guest (who sounds a bit like Jim Lad on that "Blow the Man Down" thread) - I have worked at halyards and capstans (as have many of the others on this thread), and have experienced a good amount of extemporaneous chanteying. It's not as impossible as you seem to think, and I'm sure that chanteymen who knew their business could do it very handily. There are plenty of historical sources to back this up. For example, F.T. Bullen, who was chanteyman on every vessel upon which he sailed, from 1869-1880, has this to say:
The stubborn fact is that they had no set words beyond a starting verse or two and the fixed phrases of the chorus, which were very often not words at all. For all Chanties were impromptu as far as the words were concerned. Many a Chanteyman was prized in spite of his poor voice because of his improvisations. Poor doggerel they were mostly and often very lewd and filthy, but they gave the knowing and appreciative shipmates, who roared the refrain, much opportunity for laughter. Because of this I maintain that a Chanty that is "composed" to-day by a literary man is an anomaly. (Bullen and Arnold, Songs of Sea Labour, 1914)
There are more examples I could cite, but I think Bullen says all that needs to be said on that thread creep.
Now as for Scottish chanteys, I had to give Alexandrine Smith's Music of the Waters back to the library, but I think she might have a Scottish work song or two in there. I'll try to check and get back to you on that.