To use and dropship with Oberlo, you will need to use Shopify. Oberlo does not have any other integrations for other websites.
However, Shopify does have a Lite Plan that is $9 USD a month and allows you to put the checkout on another website. If this checkout is compatible with your website host, you can still dropship with Oberlo.
Here is an in-depth guide on how to dropship with the Lite plan that you made find useful. Hope it helps!