It’s good to know that about the Sa’ami. My maternal grandmother was from northern Norway. Photographs of her look eerily like my mother-in-law. Mrs. VanShuyten is from Japan.
There's always been a question about who those people were since the DNA is pretty much hidden in an overwhelming standard East Asian package ~
Not all that long ago they pinned the Sa'ami down to WESTERN EUROPE ~ just like most Europeans ~ however, the Sa'ami have a marker gene sequence that makes their presence in other DNA very clear. The main groups to date are the Chippewa/Ojibway, Iroquois, Cherokee (anybody could have guessed those three), Berber, Fulbe, and, lo and behold, the Yakuts Sakha ~ they live today in Yakutia in Russian Siberia. This is a very different sort of Central/Eastern Asian group ~ they'd had writing at one time and kept the books. A Russian archaeologist deciphered the text and the language about 10 years back and found they'd earlier lived in India as well ~ however, this is the group that has a language and cultural symbols closest to the modern Japanese.
Japan was invaded in the mid 500's by a group speaking the now dominant language there. The islands were united into a single nation about 900 years later after a very lengthy war. Much history was lost.
The Sa'ami definitely left marks on East Asia ~ but as far as East Asians making marks on the Sa'ami that's no moreso than your average 5% found all over Europe.
There are some Sa'ami who definitely look East Asian but that's been determined to be a holdover from our common Cro-Magnon ancestry. Remember, white folk, Chinese and a whole bunch of in-betweeners all over Asia have a common Cro-magnon ancestry from 50,000 to 35,000 years ago!
You can find a recent news story on the finding that a single gene controls hair folicle shape/size, tooth shape, sweat gland number and distribution AND, lo and behold, breast size. Humans have one type or the other ~ East Asians all have the one with dark thick hair, flat teeth, more sweat glands and smaller beast size.