How to add custom theme for Add a Product page
It depends what part of the page you want to theme, simple CSS, change the layout, or adjust the form.

To add CSS, you could attach your CSS file in hook_page_build for that path.

To change the page template, you could override the page.tpl.php file as page--node--add--product.tpl.php

You could also set a custom template in hook_preprocess_page by checking for the relevant path and setting theme_hook_suggestions to your template (e.g node/add/product and node/[nid]/edit)

Another option is using hook_custom_theme to specify a whole new theme for that specific path.

Lastly, you can theme the form itself using hook_form_alter and using either a template for the form, or adjusting the form elements there.