As long as the package you need doesn't include a C extension (which most don't) you can just ship it with your code (license permitting ofc.) - just add the path to the libary to sys.path. It's not a very clean solution but can be a real life saver when you have to work on "broken" systems.
Sorry, I wasn't clear. This is a system I log into every day, and I don't want to maintain my own install of Python and related packages on it. It's too much overhead. I'd rather just use the default Python, even though it's old.
[1] I only just learned about envoy in this thread. Thanks! Sadly, one of the places where I run my Python scripts is a location where I can't install my own packages, and I don't want to deal with using my own install of Python, so I tend to just implement something like this: