First of all you should use the standard pre and code elements instead of blockquotes. But if have too many to change them, there might be a workaround.
If you only use blockquotes for code, then you can use a bit of jQuery to convert those to pre tags, but make sure to do that before Prettify is loaded.
I don’t know how the plugins work, but I can help you do it directly with Prettify.
Download it from here and enqueue it on your website.
Then use this jQuery to convert blockquote to pre and trigger Prettify.
$("blockquote").replaceWith(function() { return "<pre>" + $(this).html() + "</pre>"} );
prettyPrint();