Don't know about Hyprland but it should work generally. On KDE I have shift + the volume keys set up to only change the volume in 1% steps instead of the usual 5%.

I have had that working on Hyprland, using shift+volume to change microphone volume. First, obviously, make sure that your keyboard returns XF86AudioPause (not, e.g. XF86AudioPlayPause). Next, try having that key combination execute a command you know works (launch a browser or some such). If none of those work, I'm out of ideas.