Just to ensure we're on the same page with this, distributing pre-compiled binaries probably isn't a viable solution. Instead, I'm suggesting you distribute the versions of the module source that you've tested your tool with, e.g. DBI-1.631.tar.gz and DBD-Oracle-1.70.tar.gz (the latest versions at the time of writing). In this way, you retain control over the versions of these modules.

Then the client can install these as needed. You can retain further control over how the installation is performed by supplying an installation script. The guts of this script would probably be along these lines (which is just off the top of my head):

tar zxvf Module-version.tar.gz > Module-version.INSTALL 2>&1
cd Module-version
perl Makefile.PL
make
make test
make install
[download]

This way, you control what is installed and how. You don't need to become physically involved with the installations yourself, e.g. getting access to machines, waiting for compilations & tests to complete, and so on. The extent of that involvement, if you did it youself, would depend on your relationship with your client (which you haven't told us about): on-site or remote access; level of privileges, etc.

The client does the work but, as that only involves running a script you've provided, would probably make them more inclined to do so. It may even appear that you've done additional work for them which would likely be received positively. Again, all this will depend on your relationship with your client, so I'm guessing somewhat here.