Upgrading and creating entity references I have a Drupal 6 site which I plan to upgrade to Drupal 7, but I would like to do some alterations to one of the content types on the upgrade.

When I built the site I did not use D6 Node References on a content type when I probably should have; for example, instead of referencing a company content type containing fields for its name and website, I just have two plain fields, company name and URL.  I would like to find a way to fix this on the 'new' site.

Do I try to fix this on the Drupal 6 site then do the Drupal 7 upgrade, do the upgrade and then create the D7 entity references, or can I, as part of the upgrade, build the entity references automatically?

I'm not planning on doing a Drupal 7 or Drupal 8 data migration, so that option is out.
If you attempting a Drupal 6 to Drupal 7 update without migration, you want to keep the structures as simple as possible since minimizing rough edges. Therefore, I would wait until after the update. 

Once the site is upgraded, I would update the content types involved, and then write a simple custom module that creates a batch job for the conversion.