Is there a way to author an OCX file in Delphi 4 that makes use of ODBC to
communicate with a remote Oracle database without deploying the BDE on the
target machine ?

This OCX is going to be integrated into a system developed in another
language that has an already-overburdened profile on the target machine.

When I create an ODBC System DSN on my local machine that I'm using to
develop the OCX, the BDE Alias appears to be created automatically for me.
The ODBC mechanism works as expected.  When I take the OCX file and deploy
it on another user's machine, create an ODBC System DSN with the same name
on the target machine without installing the BDE, I receive the typical
"Read of address ..." exception message that implies that the BDE is not
installed and needs to be.