Is it ArcGIS Explorers 2D or 3D display?
If 2D, you could set the map coordinate system to be the same as your WMS service.
http://webhelp.esri.com/arcgisexplorer/1500//en/index.html#map_properties_coordinate_systems.htm
That will give the best performance as well as the best display. When the ArcGIS Explorer map coordinate system is set different from the data, it reprojects on the fly.
Mark