No, there is no standard MIDI CC for transpose or octave settings. The Nord Stage 3's EXT section includes dedicated octave controls for this purpose. Since there is no MIDI CC for something like Octave Up for example, It does this by adding 12 to every Note On/Off value that it sends. But no, this will not change the octave of things you play on the MX49 itself, which I suspect is your goal here. There simply does not exist any standard MIDI function to do such a thing. Yamaha may (or may not) have enabled their own model-specific MIDI implementation to support this, it's the kind of thing a manufacturer can choose to do using system exclusive, but even if they did, the Nord (as with most keyboards) has no ability to send sysex commands anyway.

My question is: Is there a MIDI CC message that I can send to the MX49 that will change the "Transpose" and/or "Octave" setting as well?

No, there are no MIDI CC messages that Transpose or change Octave.

Program Change (Dn) is done by its own category of MIDI message.
Volume is actually done by a CC message, Main (channel) Volume = CC7

What is available is the opportunity to [STORE] your MX Performance so that when play the Tone Generator is “Note Shifted” the number of semitones you require.

Each MX Part can be Note Shifted +/-24 semitones.
Press [EDIT] > select “02: Part” > select “Play Mode” > scroll down to “Note Shift”
This will change what pitch sounds when you trigger it… if you play middle “C” on your controller, if Note Shift = +12 you will hear the “C” above middle “C” sound from the MX.

You can STORE this Note Shift in the MX Performance.

Yes. I am trying to set the MX49 so that when I play it I am in the same tuning as my NORD, and in the right octave. I was trying to avoid creating repetitive programs on the MX49 with the same sound but different pitch settings, but I guess I will have to do this, like Bad Mister suggests.
Thank you for your help - I can stop Googling about it now. 🙂

Many controllers allow you to store the Transpose and Octave setting in the Controller. Check your controller’s documentation for master keyboard functions.

I am liking the idea of creating User Voices that have the desired pitch settings already built in. Now my question is: Where do I find the MSB/LSB/PC numbers for my User Voices?
I have the "Voice List" table for the Factory Voices, but I have not found anything for the User Voices.

I just found the answer to my own question on page 57 of theMX49_MX61 Data List.
On the MIDI Data Table it lists the User Voices located at 63 / 8 / 0-127 (MSB / LSB / PC). I can program that into the External section on the NORD now and pull up my own customized Voices on the MX49.
This is a game changer for me and will save me a lot of button-pushing during a live performance!