Welcome to the forum, Kristjanr.
So it seems as scabbards did have wooden cores.
I read out there that "XVI century ones were built with a wooden core of thin planks, wrapped in linen soaked in glue (rabbitglue) then covered in leather."
Too bad our beloved Michael (Matchlock) has passed away and can not comment on this subject; he would certainly have a say about it.
There is a chance that Jasper (Cornelistromp) comes around and may answer your questions.
Meanwhile perhaps you wish to have a look HERE
; these folks seem to be well within the matter.