You could install from an USB device too (floppy is possible too, but I guess USB stick would be easier since you have to handle only one device).
you will find the USB installer that AlienBob created and which will be included in the upcoming Slackware release. I never tried it, but I'm quite sure it will work. If you have any problem with that a question in the Slackware forum should be fine.
Steps you need to make first: Start your already running Linux, copy the "slackware" folder somewhere where you don't need to reformat. Then when booting from your USB stick you can choose to take the packages from a mounted partition. Change to console number 2 (Alt+F2), log in as root, make for example the folder /here-they-are and mount the partition with the packages there. Switch back to console 1 and type in the path to the package folder (for example "/here-they-are/something/in/between/slackware" or whereever). Floppy install works the same way but you have to create some (three???) floppies. They are on the installation CD in /bootdisks and /rootdisks (sorry, never used them, so I can not give further tips here).