Check the voltage/amperage output with your multimeter to make sure it's within a range of the intended input to the tool for you to feel safe (note: ...
Step 2: Modify (or Build) The Battery Connector
If your tool set has a carrying accessory that snaps into the battery connector like mine did, this step's easy: just cut a hole through the carrying accessory that's slightly bigger than the cord you want to run through here. If this doesn't exist for your tool, create one out of your favorite nonconductive substance or (carefully) take apart a battery and just use the shell.
I got annoyed by the nylon carrying loop thing, so I cut that off too.