SEF urls

First, you could update HikaShop to 1.5.2. We improved the SEF URLs already. If you need even shorter URLs and that you don't want to use the redirect tool of joomla, you will have to edit the file components/com_hikashop/router.php and change the code there.

I must say that I didn't use the URL redirect tool of joomla much so far so I wouldn't be able to help much on that end...

In new versions of HikaShop you can remove the shop/product page in the URL.
The category_pathway part is only displayed in some cases and is needed for breadcrumbs in these cases.

So you can have URLs like that:
www.domain.com/1-product-name

The shop part comes from the alias of the current joomla menu.
The product part comes from the option "Product SEF name" in the Main tab of the configuration of HikaShop. It will be displayed when the option "Activate smaller url" is turned on.

As I said, the product part comes from the option "Product SEF name". If you empty it, it won't display it.
The cart part comes from the your menu alias. You should change the alias of your menu to change it.
The 1-m409834p-coilsteam-rh-150170-pkg part is the id and name of your product.
If you want to shorten it, you should shorten the name of the product.
For the category_pathway-13 part is only displayed in some cases and is needed for breadcrumbs. If you don't want it, you will have to edit the file components/com_hikashop/router.php and add code like that:
if(isset($query)) unset( $query );

before the line:
if(isset($query) && isset($query)){