No. Not unless your users have given you VERY unusual permissions. No IT admin in his/her right mind would allow internal users to grant such permissions, and a public user would have to be absolutely insane to grant a website file-system privileges on the local machine.
A simpler solution would be to fiddle with your web page design so that the correct icons are shown for “known” file types. If you upload a standard set of icons as image resources, you can then link your attachment rendering code to these for a better look and feel on the web.
There are a few ways to do this, but one of the best articles is this one, IMHO: