Installing and booting most Linux distributions from an external usb drive should not be a problem. Since you have Fedora already on your computer, do you plan to use another version of Linux? That would be your first decision, then the size of your external drive, number and size of partitions, whether you want to use windows or Linux bootloader and which drive you want to boot first. You should familiarize yourself with Linux/Grub drive terminology (should be easy to do) before installing anything.
What is a Shuttle K45?