Unfortunately, non-blocking IO isn't as simple as blocking IO. I'm not sure why you say that your sockets are "defaulted to non-blocking" simply by virtue of using IO::Socket
::INET. To my knowledge, sockets created from this module are not automatically placed in a non-blocking state unless you explicitly ask for them that way.
To get around the fact that many of your non-blocking socket calls will immediately return (frequently with 'undef'), you should use IO::Select to detect when a socket has something for you, or when a socket is available to accept data. It's generally safe then to read from or write to a socket such that you won't block, and won't get 'undef' (unless it really means it).
Unfortunately this logic tends to add a lot of additional complexity to your code. Fortunately, much of this has already been encapsulated in some Perl modules, POE being the most noteworthy.