An acrylic paint pen would probably work well! Try a little dot on the back of whatever you use first x
I would just use a biro. We had a jenga set instead of a wedding guest book at our wedding recently, and biro was absolutely fine
Sharpie?
Biro as sharpie will just run and make it looked smudged
I had one of these and you’re right, the sharpies bled. In the end I just used a black biro and that worked well/showed up on pics fine 😄