If possible, you could add a style tag in the head after your link to the css file like this, which would override the css file setting.
<head>
<link rel='stylesheet' type='text/css' href='css.css' />
<style>
.existing-classname {
background-color: #ff0000;
}
</style>
</head>
Or a second css file
<head>
<link rel='stylesheet' type='text/css' href='css.css' />
<link rel='stylesheet' type='text/css' href='css_newcolors.css' />
</head>
Either way, this must be much better than running scripts, as you still need to write a list of elements to which this is to be applied, and what if scripts is temporary disabled ?
Update
As you don't wanna search/replace the existing CSS rules, and to keep the work load at a minimum level, another option would of course be to just add the replacing color rules for the targeted elements in the end of the existing css.
Doing so you don't need to alter anything anywhere, like html head tags or adding script.