There are several options besides another template. One is put the path to the CSS file to use in a template variable and use a TV tag: [*TvName*] in the template where the CSS file is specified. Using @INHERIT for the TV’s default value will make it so you don’t have to enter it on each page.
You could also use a snippet that returns the path to the CSS file. The snippet can check the Document ID and return the appropriate CSS file. Then you’d use the snippet tag in the template where the CSS file is specified.
Another way is to use the same snippet, but have it inject the CSS directly using:
$modx->regClientCSS(file_get_contents('pathToCssFile'));
With the third method, you don’t need to specify the CSS in the template at all -- just add the snippet tag to the template.