Hi /diy/, I don't usually come here so bear with me.
Is there any way to mount an extension cord to a wooden desk without damaging said desk?
I've used Velcro for many years. It allows rearranging strips and other computer shit and you can peel it off when not wanted. 2" wide is ideal. Walmart and craft stores have it or order online.
You can do very useful shit with Velcro, for example making strips to tie up your cables.
Also use zip ties to tidy up cords. You can cut them off as needed and they are cheap.
That combo of zip ties and Velcro (use Velcro brand) kicks ass.
the correct answer is self amalgamating tape (can be peeled off with zero residue because it only sticks to itself) as padding, warp it to the desk leg, add wrap some velcro as padding, then put your thing on top, then zip tie the motherfucker down tight, the velcro padding will prevent the zip tie damaging the wood, but it will be more than tight enough for the extension cord