Many image editors, especially pixel art oriented ones, support saving and importing palette files. The way to do this depends on the program you're using.

In Photoshop, if you go to Mode -> Color Table on an indexed image, you can Save and Load a palette there. However, loading a palette just replaces the actual values in order, it doesn't try to match the palette. So, saving the palette works great, but loading the palette only works if the colour order matches, which it often will not. If you want to automatically match the closest colours, you need to re-Index the image. Convert it to RGB, then back to Indexed, and in the dialog box, load your new palette as the Forced custom colours, and set the colour number to the number of colours in that palette.

I use PS which doesn't support paletted layers, and I like to keep my layers, so I can't just load a palette when I want to replace colours. So, I do change my colours by hand. Fortunately with pixel art it's pretty simple, I just need to use the Bucket tool with Contiguous set to Off, so that it fills all matching colours with the new colour. It is possible to write a script that does this automatically after being given a new palette, but I haven't gotten around to writing one myself.

I usually keep similarly-sized sprites in a single file, both to reduce disk reads in my games, and to make edits like this easier.

Mmm, indexed palettes is a great idea, i didn't thought about it. I don't use photoshop or the like because they are too complex for me, but maybe i can find the way to automate this. Thanks!