The data would need to be shown when a node is displayed - I would like the data to be accessible from within views, but also searchable, e.g. display products where stock level < 3 for supplier xyz.
How can you say I want the data to be integrated into my website -- but not imported into Drupal. Your goal sounds like alot of work.
You could try something like Remote Entity. But honestly I would take some time to learn the Migrate module and use Rabbit Hole to insert the data as "hidden" data to drupal entities or content types in my site. Migrate is super powerful for this type of syncing of data (syncing being a topic I think you're glossing over).
EDIT
You could try to:
- use hook_entity_view_alter to put content into a node view.
- use hook hook_views_data and putting your DBs into settings.php to be useable by Views displays and filters.
- use something like hook_search_api_query_alter to include your custom dbs in queries to search
... all of these in my opinion would be harder to maintain in the long run, rather than a recurring interval of updates or syncing of data using Feeds, Migrate, and storing a copy of the data locally in a drupal friendly format (eg a content type or entity).