No you are safe to equip a new buddy. I also had that problem and after achieving the required 100 candy I was free to immediately evolve my Feebas.

As credited to @yoozer8

> Note that the distance walked is tied to the specific Feebas that was
> your buddy. If you have more than 1 (or if you hatch/catch a better
> one later), you'll have to walk the one you want to evolve, even if
> you've already walked another 20km