Hi John.
What fingering have you adopted for the Bb in the key of C (C natural in D)?
The one I use on generation type whistles is
    Fipple end 0 X X X 0 X but other players on different Whistles use 0 X X 0 0 0 or 0 X 0 0 0 0.
    I think the only way to get C# and c# is by half holing.
   
   All the best PP