Laptop Cables And Docking Stations

I have a docking station at home for my work laptop, and it's all set up with dual monitors, keyboard, etc. I've just bought a new personal laptop, and I'm trying to work out how/if I can use it in the docking station to take advantage of the large dual monitors.

The power supply that came with my new laptop says 90w; the one that comes with my work laptop says 130w. So I'm guessing that means I can't just plug the cable from the docking port that goes into my work laptop straight into my personal laptop, right? They'd have to be the same wattage?

So the laptop power supply for my work laptop goes between the docking station and the power outlet. So I could just swap out that power supply for the one that came with my new personal computer and then I could plug the docking station into my new laptop, right?

Assuming that the above is right, it's gonna be a pain getting under my desk and unplugging one power cable and plugging the other one in every time I want to switch between my work and personal laptop. Is there any other way to do this?