The method that I used when limited to floppy disks was setting up an NFS server at home, and using the Slackware Linux boot floppy to load the software packages from the NFS server. This requires having a supported NIC. A good recommendation is the Linksys PCM100. (NOT the PCM200) If you don't have the resources to setup an NFS server (a bit of overkill if you'd only use it for this one process) then there are methods of installing Slackware linux over FTP, though this is a bit of a "hack." The main ones for Slackware that I know of are called
SuckSlack and
SlackFTP. If *BSD interests you more, lots of documentation is available on
http://www.freebsd.org for installing a system via either NFS or FTP. (their installer provides native FTP installation support, no hack jobs! ;-)) Here is a quick link, but you may want to do more background reading before you jump right in.
http://www.freebsd.org/doc/en_US.ISO...iff-media.html
I am sure there are many other possible ways to do it, and we all know how well linux and bsd runs on older hardware. You could even run X on this with a very low resource window manager like blackbox, or twm, but I would recommend keeping it to the CLI as much as you can. I have seen Windows 95 run very smoothely on these older laptops, but to to your limited installation method, this seems to me like the best way to go about this.
Good luck, and if you have any further questions, I may be able to help you out!