Non-IE elements in Scandinavian

As a speaker of Norwegian, German and English, I have noticed that
Norwegian (and the other north-germanic languages) have a wealth of
words which don't exist in other languages. Certainly any language
will have unique words, but there are just too many to be a
coincidence.

My theory is that when IE settlers came to Scandinavia, they had to
live in peace and harmony with the aboriginal population because of
the harsh climate here. To survive, they had to learn new skills
from the natives. For a long period of time they lived side by side,
and the Indo-europeans took up a large number of native words. Since
very few words in modern Norwegian bear any resemblance to Uralic
words, I doubt the pre-IE language was Uralic.

What kind of language did they have? Would it be possible to get a
glimpse of this (or these) ancient language(s) by searching modern
Scandinavian languages and Icelandic for non-IE elements?

Examples of unique Sc. words: fjell = mountain, jente = girl, hav =
ocean, furu = pine, ekorn = squirrel, ørret = trout, tjern = pond,
rar = strange/funny, nes = tiny peninsula, skog = forest