Italic style via contextual menu?

All the above comments can be combined as follows:

1. Create a character style, name it Italic

2. Install the following script in the usual way:

try {
  app.selection[0].appliedCharacterStyle = 
    app.documents.item(0).characterStyles.item('Italic');
} catch (_) {
}

3. In the keyboard shortcut editor, apply any key or key combination as the shortcut to the script. (Scripts are in the Scripts product area.)

A better approach to applying inline styles like italics is to use a character style. And you can set up a shortcut of your choosing to assign it. 

https://helpx.adobe.com/indesign/using/paragraph-character-styles.html

If you want to continue with manual formatting, you can change any keyboard shortcut in Edit > Keyboard Shortcuts. Apply Italic is in the Product Category: Text & Tables.

~Barb