Switch type
I have opted to provide you with a choice of Switchcraft switch depending on which your Les Paul requires. This choice is between the traditional 'long frame' toggle, or the more modern 'short frame' toggle.
A traditional long frame toggle will only fit specific variants of Les Paul, as the cavity/body depth needs to accomodate the larger housing switch itself. Some models of Les Paul, for example the Les Paul Special, will not accomodate a long frame switch. The Switchcraft long frame toggle switch internally measures 38.5mm so needs a minimum switch cavity depth of 40mm. These switches also have a very shallow mounting thread length, and you'll likely see them on Les Pauls with an extended thread mounting nut also fitted. If you select the long frame switch, I will be supplying it with this additional mounting nut for you.
A short frame version of Switchcrafts 3 way toggle I have found from experience fits within the toggle cavity of a LP much better, meaning wires aren't squished in there, and also the threaded part is much longer meaning you won't need an additional recessed nut to fit. You can use the spin on nut provided with the switch. This spec switch comfortably fits all varieties of Les Paul models.
Wire type
Depending on your intentions/preferences, I now offer the LP toggle switch harness wired 'traditionally' with outer braided wire, or with prepared braided wire alongside cloth covered wire and a separate ground to simplify the install process. Neither is superior to the other, it comes down to your preferences, what wiring style you have in the guitar already or perhaps your intentions for the re-wire.