If the player has a good ear (and you're not asking them to do really virtuosic playing), then the "embouchure shock" should be fairly minimal.

As long as they're still reading transposed treble clef music, the fingerings will be exactly the same, with the notable exception of french horn (or is that a brass band instrument to start with?). Tuba doesn't read treble clef traditionally, but a treble clef, transposed part could be easily created that would work just fine for the player.

If the player is brand new at brass instrument doubling, then yes, they may need a few days to get used to it, just for the fact that it's different from a cornet. A more experienced doubler can usually switch around at will with no "adjustment period".

What brass band instruments can a cornet player feasibly cover on short notice?
John 19:38 - 40 (NLT)


  38 “What is truth?” Pilate asked. Then he went out again to the people
  and told them, “He is not guilty of any crime. 39 But you have a
  custom of asking me to release one prisoner each year at Passover.
  Would you like me to release this ‘King of the Jews’?”
  
  40 But they shouted back, “No! Not this man. We want Barabbas!”
  (Barabbas was a revolutionary.)


Why were they so messed up that they would choose the rebellious, murderous Barabbas over the innocent Son of God?
