Changing the size of the audio volume increment of the "volume up" / "volume down" keys
Yes a third-party app seems to be the best solution.
Microsoft's response to the problem is this;
The keypresses are sent to the OS as APPCOMMAND_VOLUME_UP and APPCOMMAND_VOLUME_DOWN HID messages. These are then translated to calls to IAudioEndpointVolume::VolumeStepUp() or IAudioEndpointVolume::VolumeStepDown(); this is hardcoded to 51 steps.
Possible mitigations are to toy with the keyboard refresh rate in the Control Panel or to write an app that listens for the APPCOMMAND_VOLUME_UP HID messages and does its own thing.
Some laptop manufacturers provide a third-party application that captures special keypresses and provides OSD etc, and this might be customizable.
Otherwise I'd also recommend 3RVX as per your comments.
In contrary to the OP my aim was to reduce the increment from 2% to 1% for my in-ear-phones. My workaround without having to install 3rd party software was to reduce the volume of the source (e.g. media player) to 50%. Since final volume = source volume * taskbar volume the 2%-steps are now effectively 1%-steps (I never need more than 20% of the max volume)
You can use the open source 3RVX program:
Settings
Hotkeys
+
Keys
Action: Increase Volume
Amount: 10 Percent
Note that 3RVX also has skins beyond what comes with the release. For example, I am using the “Windows Default” skin. What is also useful is that you can customize these skins by modifying the skin.xml file. I changed mine to increase the font size.