Stale Pathauto Alias
You should use Pathauto if you aren't already. 

This has a feature (tab) that lets you bulk update the content type urls to /widgets/[node:title].

You should also install the Redirect module, so that all your former /products/[node:title] automatically redirect to /widgets/[node:title]. This is for SEO purposes, you don't want your Google listing pointing to a broken link, non-existent page.