You can boot from Slackware DVD and install it to the external hard drive directly.
Boot from DVD with a parameters by default, plug in your USB-HDD, then, make sure that your USB-HDD is available:
Then, prepare this:
where /dev/sdb is your external hard drive. Prepare a few partitions: for '/' (root directory) and swap. This is minimal for working. Swap partition should have a dimension according to the RAM capacity. For example, you have 2 Gb RAM, then swap should be same.
Then, just type 'setup' and follow the on-screen instructions.
Do not install lilo, just completely the installing, and install lilo manually:
Something like this.
P.S. Sorry for my english.