Most Western states had more transplants than direct immigration. Though two exceptions come to mind.
North Dakota: Not officially the West, but it's a Great Plains state that most closely resembles the Canadian Prairie provinces. I think it had the highest foreign born share of any state in the early 20th century, mostly Germans from Russia and Norwegians.
Utah: A lot of Mormons immigrated from England in the 19th century. I used to think English ancestry was high just because Mormons are really interested in genealogy, but in fact Mormonism had a lot of converts in the UK. I think the number of American transplants and British immigrants was about equal in Utah.
California seems to be a state strongly associated with transplants (even up to today), alongside Florida, although both places have lots of new immigrants directly arriving currently too. I'm sure there were lots of immigrants and transplants alike who chose to go to California after it became part of the US (during the Gold Rush period), since the number of Californians who descend from prior to that time (eg. when it was part of Mexico) seems quite low. I find it interesting that despite the fact that the US has a lot of territory that used to be ruled by France and Spain (eg. before the Louisiana Purchase), there's no analogous region (except maybe New Mexico) in the continental US to Quebec, where a majority or large proportion of people descend from pre-Anglo-American settlers.
There are a lot of Scandinavian Mormons, such as Norwegian, Swedish and Danish, too -- if I'm not mistaken, it's a similar story to the UK, mostly converts who later moved to the States.
How about Canadian Mormons -- did they mostly descend from converts or American settlers? I know Alberta was settled quite early on by Americans and include some of the earliest Mormon settlements in Canada, but I'd assume many in places like Toronto converted much later.
And since the 1940s, Ontario has gained Ukrainians relative to the Prairies, although a majority of Ukrainian Canadians (around 60%) I think still live in the Prairies.
Was this gain from moving to Ontario from the Prairies, or from direct immigration from Ukraine?
A few things:
Brazil and Peru have quite large Japanese populations.
Note that not all Chinese immigrants are from China! Countries as disparate as Thailand and Jamaica both have significant Chinese populations and both groups have immigrants to Canada bypassing China completely.
I don't know much about Peru, but the Wikipedia article on Chinese Peruvians claims that hundreds of thousands to over a million people have some Chinese ancestry. Have no idea how accurate the sources would be, but the high end of that estimate (1.3 million) would place it on par with the number of Chinese Canadians, which would seem surprising.
However, I'd imagine that the Chinese ancestry of Peruvians came from much earlier in history and there'd be lots more people of partial or more distant Chinese ancestry there than in Canada.
https://en.wikipedia.org/wiki/Chinese_Peruvians