Cool, do you use cura's post process for that?
Nope... I just paused it in Octoprint.
My first attempt involved moving the head off of the print to swap the filament (I wanted to be able to clear the nozzle) but it didn't register the movements correctly on the way back so it was off when I unpaused. On the next attempt I just made sure I paused the print while it was over an infill area so that any filament creep would be over that instead of making a mess of a wall.
While it was paused I pulled the filament back about an inch or two, used a wrench to undo the fitting on the extruder and cut the existing filament at the edge of the fitting. At that point I used a piece of filament to push the existing colour filament into the bowden tube until I felt a slight resistance (indicating that it was in the hot end) and fed the new colour filament through the extruder and into the tube. I then re-attached the fitting and advanced the new filament until I felt some resistance, and "unpaused" the print through octoprint.
In hindsight, I probably could have just removed the initial filament all together and then just inserted the new filament until I felt resistance.