yorozu

The searching is narrow down a search depends on custom field you saved. 
So, it’s basically avoid a not found. 
You’d like to use in widgets.

Search Refinement

Just another search refinement plugin depends on custom filed.

mattsgarage

The search functionality in woocommerce doesn’t search by sku by default.
This simple plugin adds this functionality search facility of your site, in both the public site and admin panel
Just install and activate – no config required.
Tested with Woocommerce 1.5.6, 2.0.7, 2.0.18, 2.2.4, 2.2.10, 3.4.4, 4.0.1 and 4.2.0
See the <a href="http://www.mattyl.co.uk/2012/12/11/woocommerce-plugin-to-search-products-by-sku/" title="accompanying blog post" rel="nofollow ugc">Accompanying blog post</a> for more information.

Search by SKU for Woocommerce

Extend the search functionality of woocommerce to include searching of sku

Search Refinement vs Search by SKU for Woocommerce