There are multiple ways to do this:

1. Set NVDA to go through the headset, and your system audio to go through the speaker.
You can do this from Settings (Windows+i), System, Sound.
As you arrow through the list of output devices, your system audio will change. If you don't want NVDA brought along, SET IT TO YOUR HEADSET FIRST.
If you don't want the output device to change as you navigate, press alt down arrow to open the combo box, select your device and press enter.
2. If you don't want all your system audio going through the speaker, your music player might have an option to change the output device.
3. Windows has a feature in the sound settings to move one app to another audio device.
Here's how to use it with NVDA.

From the sound settings, select App volume and device preferences. Once that opens, tab to the list.
This is a list of apps you can change the settings for, so select your music player.
There's a mute app button and a volume slider. After that is the output.
If you arrow down in this list, you'll probably end up on the "Reset to the Microsoft recommended defaults." button. Once you end up there, if it didn't change to the right card, you'll have to go all the way back to the list and re-select your app, then go back to the output and arrow down again.
One way around this is to press alt down arrow on the output combo box, then select your sound card with the arrow keys and press enter. You'll still end up on that button but you can navigate the output list without having to go back all the time.