You would need to give us the exact laptop model, however my advice is this:
1. Go to the laptop support site
2. Locate the appropriate VIDEO software and download it
3. Uninstall your current video software
4. Install the downloaded software.
I've never used a setup like that so I'm uncertain what software is involved. You likely need at least two pieces of software. For example, you may need the Intel drivers, the NVidia drivers, and a separate piece of software to handle the SWITCH between them.
Other:
Your Switchable graphics software should have an option for you to manually add programs to it. Skyrim should have been detected, however if you use SKSE (which you should to get SKYUI working) you'd need to launch the SKSE...