I wouldn't.

Just create classes that delegate to DBI and wrap DBI, potentially via AUTOLOAD. You will need:

1. One DBI-delegator, mainly implementing ->connect , returning
2. One DBH-delegator, mainly implementing ->prepare and ->do, likely via ->prepare->execute, and
3. One STH-delegator, mainly implementing ->execute and ->fetchall_*

I would stay away from inheritance and just store the DBI::* instances, as you seem to be mostly interested in the user side of interactions and not so much in actually modifying the behaviour of DBI and its components.