This may be a little like buying the whole kitchen sink just to get the faucet knob, but Mojolicious contains Mojo::UserAgent, which can be used as a non-blocking event driven User Agent. The Mojolicious::Guides::Cookbook contains a section on "Non-blocking" User Agent examples.

I think the whole Mojolicious distribution is around 2-MB, which is a lot for just a user agent, but trivially small if you have a use for the other features as well. Plus, it has no external dependencies (one of the Mojolicious design goals, which some consider "a good thing").