If you have specific symbology which you made in ArcMap, the way to use it in ArcGIS Explorer is to put the symbols you want to use into a style file, then turn that style file into a ServerStyle file - this is the format used by ArcGIS Explorer (and also by ArcGIS Engine and ArcGIS Server). See http://forums.esri.com/Thread.asp?c=184&f=2208&t=222414&mc=4#msgid674498 .
Once you've got the server style file, you can distribute that to the Explorer machines that need to display the shapefiles - existing Style files live in \Styles. The new style should now be available - when you add content, in the final page of the Wizard where you choose the symbol, click the Styles button and you should see your new style listed, and once it's selected, you should see the symbols in the list box above.
Note use 9.2 ArcGIS to create the style file - not 9.3 beta if you have it as ArcGIS Explorer up to the current release might not read symbols from a later version of ArcGIS. I've not tried this with the whole range of possible symbols, so let us know if there's a specific type of symbol that you can't use sucessfully like this. I had problems with multilayer symbols for Points, but polygons and polylines drew with multilayer symbols fine.