I can see the need of retrieving tarballs of svn repositories without having access to an svn client. But I don't see why would you need to get those to old computers.
You probably won't do development there, since that would require an svn client anyway, so you could commit your changes back.
You probably don't need to get the repo tarballs onto those computers for building stuff from those sources, because you don't need whole svn repos for that, just snapshots of certain revisions.
Since you talk about browser usage, I have to assume that those old unix computers are networked. So you could just retrieve the svn repos using another computer, create tarballs and serve them yourself from there over HTTP.
Also, if you have scripting languages installed on the old computers, perhaps you shall look for a svn client written in those languages. There are svn bindings for Perl and Python at least.
Finally, you can use those bindings to write your own trivial svn client that would do the checkout.