Yes it's possible. Go to your User Preferences, Section Input, and navigate to 3D View, Object Mode:
Then, add a hotkey for Object Mode only, and use these settings:
- Operator Name: wm.context_toggle
- Hotkey: F4
- Context Attribute: object.show_wire
This Operator allows you to toggle many boolean properties if they are accessible reliably via Python. You can test it by going to a Python console and typing in:
The object.show_wire part is referring to the Active Object, searching for a property called show_wire on it. so if you try this instead, the X-Ray Property will be toggled instead:
If you want to have the operator working for any mode in the 3D View, add the shortcut under the 3D View Global section.