This short thread has lain forgotten for 11 years. Reviving it after all this time in order to call somebody an idiot seems a little odd. For all I know, Dick, the person you heard singing may indeed be an idiot; but if he is, it's not because he sang 'blue' where you thought he ought to have sung 'white'. There are many past discussions here that deal with 'The White Cockade' which you can easily find for yourself, but it looks as if you need some special help with this particular point.

The song is number 191 in the Roud Folk Song Index; it was clearly very popular in its day given the number of versions that survived in oral currency well into the 20th century. Although white is the most common cockade-colour, there are examples in which it is blue (Williams, Hammond collections) or green (Sharp, Baring-Gould collections). While I was away checking some facts, Diane has posted Frank Purslow's note from The Wanton Seed, which is reasonable so far as it goes, but will be expanded upon in the revised edition currently in preparation. I quoted Frank myself in thread Origins: Regiment - Orange and Blue, where the discussion was mainly about cockades.

The words you quote are the ones that Napper & Bliss use, presumably, Diane? As you know, I tend to be wary of using revival arrangements to make points about any song unless we know where the performer got it from and can tell how much they have edited it. Perhaps Tom Bliss will enlighten us later on.

The song has been re-cast from time to time under more than one title, but usually to a limited extent only so that examples can still usefully be considered together as a group. There are broadside editions of various forms from the late C18 onward at  Bodleian Library Broadside Ballads. For what it's worth, the earlier ones there tend not to be 'white' versions.

[The] White Cockade

The inconstant lover; or, The Blue Cockade

Bold Light Horseman (in which the cockade is blue).

The Light Blues (in which the cockade is black).

Of course there are other, quite different songs called 'The White Cockade' , and others that were set to the well-known tune (which appears to be older than the song in question here). We needn't concern ourselves with them. 'Show of Hands' are not my cup of tea, so I have no idea where they got the version that Dick mentioned. I would hope that they say in their sleevenotes.