Displaying data from a web service
It sounds like your question cannot be answered unless it is redefined.  Drupal entities, views, and all of the other niceties that you would like to do involve storing information in the database.

You might look more closely at your regulations, and see what specifically they allow you to do.  For example, sqlite stores its entire database in a file. If you used an sqlite database where the database file was stored in a volitile storage device (e.g. a RAM based filesystem), would you still meet regulations?

Even if this is possible, you might have performance problems if the amount of data you need to store is large, because sqlite was designed only for small databases, and is mostly used for testing.  The same idea might work for mysql or postgres, though, as ultimately even these databases store their data in files.

If your data retention regulations are strict enough, you may find that the technique you are currently employing is the best you can do.