Is there a way to get a line editing function using the arrow keys just using POSIX (or some other standard approach) without access to any of the extended functionality provided by CPAN modules?

Of course. How do you think the author of Term::ReadLine and friends did it? Of particular interest to you might be Term::ReadLine::Zoid, a pure-perl Term::ReadLine implementation.

So perhaps you've guessed by now: There is no functional Term::Readline or Term:Readkey on these systems, and I cannot install one.

Bullshit. You just haven't figured out how to install one yet! Hell, if you succeed in your attempt to reinvent Term::ReadLine you'll have done it via the hardest possible route - recode it by hand! Here's a few easier possibilities:

• See if you can get PAR to work in your environment. PAR lets you bundle scripts with the modules they need. Might work, depending on how crippled your Perl is.
• Copy code from useful modules directly into your scripts. Some modules will need massaging to work like this (if they use __DATA__ or AutoLoader, for example) but many will work just fine. If the module you need has XS pieces you'll need to cross-compile them and ship the built shared-libs with your script.
• Do a detailed estimate of how much time you're expecting to waste working around the lack of a reasonable Perl development environment. Present this estimate to The-Great-and-Powerful-Code-Image-Builder-Who-Cannot-Be-Argued-With's boss. Explain in excruciating detail exactly how much money is being lost due to his policy on Perl module installs. Who knows, maybe he's not so powerful!
• Find a new job. Coding in Perl without CPAN is a foolish waste of time with very little to recommend it.

-sam