Maybe something like this:
(defun rasmus/org-html-wrap-blocks-in-code (src backend info)
"Wrap a source block in <code><pre><code class=\"lang\">.</code>"code></pre>"
(when (org-export-derived-backend-p backend 'html)
(replace-regexp-in-string
"\\(</pre>\\)" "</code>\n\\1"
(replace-regexp-in-string "<pre class=\"src src-\\([^\"]*?\\)\">"
"<pre>\n<code class=\"\\1\">\n" src))))
(add-to-list 'org-export-filter-src-block-functions
'rasmus/org-html-wrap-blocks-in-code)
(setq org-html-htmlize-output-type nil)