I would personally attach the lanyard to my daypack or backpack and not have anything else on my neck. But that's just me. It would conflict with my other stuff, especially the chest strap.

I use a shoulder strap clip for my GPSr and a separate clip for the hydration tube, then a lanyard for my whistle tucked into the pack lid. I don't use my compass [20 yr old Suunto MCA] as much any more except as a backup (yeah yeah, chastise me later! )

You could use paracord without the inner strands to tie the compass to a belt loop or pack strap or as a lanyard around your neck. Paracord without the strands is pretty stretchy but still way stronger than you ever need for this purpose and would give a little if you ever snagged it on a tree branch thus preventing stangulation. The alternate is to use elastic cord as a lanyard. That might keep it from tangling up with the rest of your gear. The problem is, I don't know if the lanyard hole on most compasses is large enough to put paracord or elastic cord through it, only way to know is to actually try it.