I think I have found at least a part of the answer.
In the article with interview in The Independent from the 3rd of May 1997, you can read this:
http://www.independent.co.uk/life-style ... 59348.html
"With characteristic Stakhanovite energy, Rea has a whole new album of jazz-blues tracks, entitled The Blue Cafe, out in October. And on Cup Final day, as the Middlesbrough crowd sing along to "Let's Dance", he is flying to Dresden, to give his first concert in five years."
I assume The Man's So Cool was recorded that time, on this Dresden performance, being a one-off non-album song, like This Kind of Love from Glasgow 1994. I thought the 1st CR gig after he fell ill in spring 1994 was Donauinselfest in Vienna on the 21st of June, 1997, but I cannot judge if it was a fulltime gig in Dresden or just this mentioned Chicago session (on TV/radio?) or both of them... but this track on Square Peg single with a sticker "incl. previously unreleased live track" was apparently recorded in mid May during the 1st CR live session after illness.
Moreover, you can see from the article that Blue Cafe was to be released 3 months earlier than it was in fact and to become a jazz-blues album! Overproduction an compromise again?.. I recall Chris first mentioning plans to steer away from commercially successful albums and make a jazz-blues record back in 1988, just before Magnet was eaten by WEA... And I have counted only about 10 CR tracks released before 2001 which seem to be close enough to what can be called a blues... So strange...