Perhaps an earlier Chinese Exclusion act that diverts some immigrants from America to Peru?
About the impact... I’m not really sure. I think they would assimilate (as they adopted local surnames and OTL). You would have to keep a steady flow of immigrants to form larger “blocs” of Chinese or Japanese cultures.
Didn’t Peru have a President of Japanese ethnicity anyway?
Yep we did, and he was a massive scumbag, but what's new in Latin American politics.
My understanding of Chinese immigration to Peru is that it was quite similar to the American version; they built infrastructure and worked plantations as glorified slave labor that transitioned to free laborers, Peruvians were distrusting of them, eventually blocked further immigration. They were also almost exclusively men, so there was a fair bit of extra tribalism involved but since they married mostly native women, the white/mestizo elite largely ignored them. Peruvian opinion turned against them when they led a pro-Chilean uprising during the War of the Pacific that led to Peruvians blaming them for the loss of the war, resulting in pogroms until the 1890s and a ban on Chinese immigrants until the 1970s. Prior to and post-pogrom, the Chinese integrated quite well into Peruvian society when they managed to escape their slave labor through marriage. The vast majority assimilated demographically bar some cultural customs.
It's not hard to keep the Chinese immigration flowing. Either avoid the War of the Pacific or have the Peruvians win, meaning that the coolie system stays in place for longer. The Chinese did a lot for the Peruvian economy and they integrated demographically with the general populace so it's likely that once the coolie system ends, it'll be replaced by continued immigration from China and a demographic transition from a largely mixed and integrated Chinese populace to a spectrum of integration into Peru now that there's significant Chinese communities that are bringing spouses with them.
I think the overwhelming majority of the Chinese community being demographically entwined with native Peruvians is going to see most Chinese eventually marry into the local demographic base given time; the Chinese community will likely become more 'Chinese' and distinct but inescapably bound to other Peruvians in terms of demographics and marriages between Chinese and non-Chinese will remain common. The Chinese community will also be less 'othered' by Peruvians and so there'll be a disproportionate tolerance for Chinese immigration to Peru compared to its neighbors, even more so than OTL.
In turn, I think the increased economic prosperity of Peru will help it be a larger target for immigrants than OTL from Europe. Assuming minimal butterflies from continued Chinese immigration, then I'd expect a very large number of Chinese to make their way to Peru over the course of the late 19th century onwards every time there's political upheaval in China due to being the only country in the Western hemisphere where Chinese would be 'welcome'(relatively).
End result, I think you can significantly increase Peru's population than OTL. I'm talking a doubling. I'd also expect a majority of the Peruvian population to have a Chinese ancestor by the present day.