Magic Keyboard and Mouse with docking station

Hi all.

I have 2 macbook pro and I'm using them aternatively (work/personal) connected to a docking station (linked to monitor, webcam and wired keyboard and mouse). I wanted to go wireless on the keyboard and mouse so I was thininking on buying the Magic Keyboard & Mouse but I learned they cannot pair with 2 devices… Do you know if there is any way to have them “pairing” with the docking and thus working with the connected MacBook?

Any of you have a similar setup? I would love to hear how you have approached this!

Thanks!!