A couple of ideas (these are comments, the suggestions haven't been tested):
1. Load the MrSID in ArcGIS and use a Define Projection tool and set the projection to ArcGIS's definition of WGS84,
-- OR --
2. In ArcPad use the Define Datum Transformation tool.
- Specify WGS_1984 and D_WGS_1984 as your Datum 1 and Datum 2 respectively
- Choose a transformation method, say, Geocentric_Translation
- Set all the parameters Dx, Dy, Dz, Rx, Ry, Rz, Xcr, Ycr and Zcr to 0