Tool to change file modified date with a tool which works inside File Explorer?

This one is freeware, and will change what you need plus various attributes that users don't normally have access to:

  Attribute Changer
  http://www.petges.lu/

You can use File Date Touch - Windows version of UNIX touch command

I know its probably too late to answer this, but apparently this http://stefanstools.sourceforge.net/SKTimeStamp.html does exactly what OP wanted:

SKTimeStamp is a very simple shell extension which adds a new tab to the Explorer properties dialog. On that new tab, you can change the file/folder date and time.

Available for x86 and x64 Windows systems.