I need to perform a schema update using a connection created my code, and the SchemaUpdate class does not have a constructor 'SchemaUpdate(Configuration cfg, Connection connection)', like SchemaExport has.

After looking at the code, I see no reason for this. AFAICS SchemaUpdate can have such a constructor, using the SuppliedConnectionHelper, the same way SchemaExport does.

Please let me know if you need more info.