Lukas-K I have a couple of ideas. Everything’s a compromise so it really depends on what’s acceptable to you. Nothing will be as good as a proper headlamp. Even carrying a light headlamp on your head gets old pretty fast. I don’t see having a heavy pocket knife headlamp on my head as something I’d plan to use in anything but an emergency.
Have you considered using one of the existing Lite models and developing a clip for a hat or head strap that allows you to have the knife facing forward on the side of your head above your ear? That would be super simple and just good enough. I’ve been an a fireman in years past and that’s how we carried our head light. That’s what I’ve thought of doing and one of the reasons why I’ve made a custom knife recently with a lite.
If you want something brighter could you modify the standard Victorinox lite module or 3d print some kind of a replacement that fits in that position in side the knife? There are lots of models with the lite module on them.
I would look around at different headlamps then buy the smallest ones and pull them apart out of their housings and make a 3d printed scale that fits the parts you need. Incorporate a small plug port for an external battery pack if you need to. But if you’re carrying a headlamp battery pack why wouldn’t you just carry a headlamp? Just saying?