To grant to work int both os with ctrl as windows ctrl is also possible simply (with macOS 10.12 and Parallels 12):

Invert Command and Control key in Mac Os:

1) Open system preferences.

2) Click Keyboard.

3) Click Modifiers Keys

4) Invert Command and Ctrl Key

4) Close preferences.

In Parallels Preferences:

1) Open Parallels and go to Preferences.

2) Remove all Virtual machine shortcuts

3) Add the shortcut: Cmd to Ctrl

-- (note that now Cmd is Ctrl in Osx so this command is simply Ctrl to Ctrl!)

4) Add the shortcut: Ctrl to Win

-- (note that now Ctrl is Cmd in Osx so this command is simply Cmd to Win!)

Now use Ctr+left, Ctrl+right, Ctrl+X, Ctrl+C.... with same "windows" use in both os.