Because the data is US data, Clarke 1866 = NAD27. It's still possible that their data could be NAD83 or a mix of NAD27 and NAD83, mislabelled. This is because Clarke 1866 was used as a default spheroid/ellipsoid in ArcInfo workstation.
You might try to push them a little--can you get some data that you can use to check your converted data against?
If we assume that the data is really NAD27, and convert your data so, but their data is really NAD83, and just mislabelled, the data could be off a hundred meters.
Let's assume their data is NAD27.
There are transformations that convert directly between NAD27 and WGS84, but they're not the most accurate. What you should do is WGS84-to-NAD83-to-NAD27. The project will only show you the NAD27/WGS84 transformations.
However, we can use a new 9.2 tool to make a direct transformation between NAD27 and WGS84 using the NADCON conus file. The tool is, "Create custom geographic transformation" and it's in the projections and transformations section of the data management toolbox.
Start the tool. Give the transformation a name, and choose Clarke 1866 (it's in the spheroid-based folder) for the input coordinate system, and WGS 1984 for the output coordinate system. This is opposite what you want to do, but the transformation will work in both directions. For the method choose NADCON. For the Grid Dataset Name, use "conus" (no quotes).
Once the transformation is defined, use the Project tools to convert your data.