Then I would just reproject the GCS version of the DEM to the cell size you want and skip the resampling step altogether. Do this in the Environments tab for the Project tool in Arctoolbox, there are a whole load of raster settings that can be made there. In fact they are the only environment settings that I rely on. I presume that if you aren't in the U.S your X, Y coordinates will be in metres, but I would also confirm the Z values from source as well. When projected, proceed with Slope, again setting the cell size, snap raster etc in the Environments tab of the Slope tool