You could look into the directory usb-and-pxe-installers in the root directory of your Slackware ISO image.
To do that, mount the ISO image using the loop option (as root). e.g.:
mount -o loop slackware-dvd.iso /mnt
The content of the image will then be accessible in /mnt.
Don't forget to umount it when you're done.
I used /mnt in the example but of course you may use another directory if you prefer.
PS I had a similar problem but the other computer couldn't boot on the usb key, so I used PXE install instead. But if it works for you you'll be better off using the usb boot, it's a lot simpler.