Old question, but none of the answers seem correct.
From what I can say, trying to make an unset proxy to run this in one of my mailboxes, I got this error: wget: could not resolve the host address' webproxystatic-mywork.com
It looks like apt-cyg is using wget. So this brings you to this question: setting up proxies in wget
The answer to this question is: set (or in my case unset) http_proxy / https_proxy in /etc/wgetrc :
# You can set the default proxies for Wget to use for http, https, and ftp.
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