Third version in reaction to comment (actually off-topic for TeX.SX in my opinion):
For selective connection settings you can install a local proxy server. I never needed one, so I cannot say anything about these, but well-known, renowned examples are Squid and Proxomitron (if you are by any chance German: Der Proxomitron - Deutsche Distribution).
I would actually recommend not to change anything,
but I see only one way without any guarantee that it works, in fact there is a high chance, that this breaks the whole update process (edit: yes, confirmed by wlnirvana in comment below):
Then, every request to
api.miktex.org goes to your local host, i.e. your computer, instead.
First wrong version, just written for expression of what was written in comment:
What Ulrike wrote – do not choose the option “Use the nearest package repository.”, but one of the two other options in update dialogue, and MiKTeX will directly connect to the chosen mirror: