Huh? Your docker container shouldn’t be calling pip for updates at runtime, you should consider them immutable and ephemeral. Build your container (presumably pip-ing in all the libraries you require) on the machine with full network access, then export or publish the container image and run it on the machine with limited access. If you want updates, you regularly rebuild the container image and repeat.

Alternatively, even at build time it’s fairly easy to use a proxy with docker, unless you have some weird proxy configuration. I use it here so that updates get pulled from a local caching proxy, reducing my internet traffic and making rebuilds quicker.