I’m hijacking my own thread to talk about transcribing for different whistle keys, so anyone is welcome to skip this post and continue reading and answering the original Q & A thread below. 
I only know enough music theory to be able to muddle along. MuseScore does most of the work for you. It’s a free program available at https://musescore.org/en . There’s a learning curve, but it’s worth it if you want to arrange your own sheet music. Note that the program itself is free from the .org site. The MuseScore.com site has music available to download, but there is a membership fee. You do not have to join the .com site to use the free program. You can also download ABC notation from a site such as TheSession.org and import it into the MuseScore program, all of which is free.
… but I gather that playing a Bb whistle as though it were a D whistle naturally transposes without alternate fingering.
Exactly. I’m new to whistle, but I believe you can play any whistle, in any key, with the same fingerings as a D whistle. When you’re playing solo, the whistle’s pitch doesn’t matter. But when you’re playing with a backing track or another instrument, that’s when the music needs to be transposed so that the pitches match. However, you can still read the whistle part as if you were playing a D whistle, as long as it’s written that way.
I’m a little more unclear on how you play in Bb (say) on a baritone ukulele, but perhaps it doesn’t matter if you’re playing individual notes rather than chords?
My friend simplifies the chords that are not uke-friendly. For example, she might play an arpeggio on three strings rather than all six, and she often plays individual eighth notes rather than strumming. The keys don’t matter all that much because she reads numbered tabs output from MuseScore.
If you don’t mind my asking, are you writing original music or arranging existing songs for whistle and ukulele (and, fiddle, harp, etc.)?
We aren’t composing our own music from scratch, although we might write supplemental parts to augment a score. Here’s an example. I started with this piano piece: https://musescore.com/user/27057308/scores/5362835
I changed the instrument to harp rather than piano. I extracted the top treble clef notes for the whistle melody line, another task that MuseScore automates. The original key is Eb major (3 flats), so I transposed everything to D major (2 sharps) to fit on a D whistle. I duplicated the whistle part, and then transposed the second whistle part and the harp part to Bb major (2 flats) for the Bb whistle. I’m reading and playing the first whistle part, which is in 2 sharps, but that part’s audio needs to be muted. The only whistle part that plays audio is the Bb whistle.
At that point, I sent the file to my friend, and she wrote her uke part. From that link above, you can see how portions of the piano’s bass clef line would translate well to fingerstyle guitar or ukulele. In other sections, she composed her part based on the harmonies.
That gives you an idea of what’s involved, and it doesn’t take that much time to do. My friend and I have been using MuseScore for about 2 years now. Playing with that program is almost as much fun as playing whistle. Where it has really helped us learn the music is being able to slow down the tempo for playing along with the tracks. That makes it a great learning tool, and it’s a lot more fun than playing with a metronome.