From what I understand, you wouldn’t be able to do this anyway even if the cord were removable. Apparently, the Studio Display is too thin to use a standard cord, so Apple created a proprietary power cable, which is probably why it’s not removable. Losing such a cable would leave you with a bricked monitor.
So even if you could remove it, you’d still have to take the cord with you to the other desk because it won’t work with any normal power cord. Or you’d have to ask Apple if you can buy a second cord, but those do not appear to be available for sale.
This is only really a problem because they build the power supply in. This also produces additional heat, which means the display always has fans running.
I'm not sure that's the tradeoff I would've picked. Just give it a small power brick. The display runs cooler, and the cable can be a simpler, standard one.