I would compare the proj strings for WGS84(DD) and WGS84
Since your data is defined in that way, ArcGIS can't find an appropriate transformation.
I'm guessing one of two things:
1. Your WGS84(DD) data is simply mislabeled as that GCS. Use the define tool to re-define the GCS to the proper WGS84.
2. Your data is actually WGS84(DD) (seems unlikely), and you've had some unknown level of error in your project.
In any case I'd thoroughly test the output. Hidden datum issues can get you into trouble depending on your accuracy needs.