Since the API is returning the HTML code and you get it as a string.
Why not just add a line to the <HEAD> of the retuned HTML code that contains the link to a CSS file on your website (ie "<link rel="stylesheet" href="
www.mywebsite/custom_styles.css"/>") ?
Then when you load the HTML code into webview it should be able to use the external CSS file to resolve the CSS references.
Keep in mind, that if the HTML code contains any javascript, that would be a totally different issue that would need to be resolved.