nOOOOOOOOOOOOOOOOOOOOO don’t do that. You need to use the Project tool in ArcToolbox, in Data Management Tools>Projections and Transformations>Feature>Project. Use this in ArcMap or ArcCatalog to select your original shapefile and specify the output shapefile and projection. You will quite likely also need to use a Transformation from the transformation drop down menu, to find the right one it is best to get an understanding of the EPSG database, though there are ‘standard’ ones, for example if you are going between British National Grid and WGS84 the ‘Petroleum’ one will see you right unless you are requiring mega-preicision.
Without using a transformation you can introduce shifts into your data, for example going between BNG and WGS84 you can get a nice 100m+ shift in data if you don’t use a transformation, which can really mess things up later on.
Lack of understanding of coordinate systems and transformations is the biggest problem I come across as a GISser, worth getting right from the start to save you going back later.