You can integrate Swagger a couple of different ways. For barebones support, you can use the ODataSwaggerConverter provided by OData. This will effectively convert the EDM to a Swagger document. To wire this up to a Swagger generator library like Swashbuckle, you just need create and register a custom generator. The UI and client side of things should remain unchanged. If the generated Swagger document isn't sufficient, the base implementation of the ODataSwaggerConverter is still a reasonable start.
If you're using API Versioning for OData with ASP.NET Core, you need only add the corresponding API Explorer package. Swashuckle will light up with little-to-no additional work on your part. The ASP.NET Core with OData Swagger sample application has an end-to-end working example.