For a standard installation of the Ardfry PSD Codec (which typically uses an Inno Setup or similar wrapper), silent installation can usually be triggered via the command line using the following switches:
This naming convention usually indicates a "repack" or "silent installer" created by a third party, not the original developer.
reg add "HKLM\SOFTWARE\Classes\.psd\ShellEx\BB2E617C-0920-11d1-9A0B-00C04FC2D6C1" /ve /d "" /f
Let's break down the options used: