Here is how you can uninstall and reinstall Skyrim quicker (only works if you haven't uninstalled the game yet). This guide applies to any other Steam game as well. Follow the steps below and whenever you decide to reinstall your game, it will be a lot quicker.

1. Go to wherever your game is installed (it is likely under 'SteamLibrary\steamapps\common' in your files)
2. Scroll to the file that says the title of the game you'd like to install
3. Rename the file to whatever you want. You can just add a letter or number to the end.
4. Uninstall your game from Steam.
5. Shut down Steam. (Make sure your right-click on the icon on your taskbar and click 'Exit Steam' instead of clicking the X on the top right of your screen. This will do a complete shut down of Steam).
6. Rename the game file to what it was before you changed it.
7. Open Steam. Whenever you want to reinstall your game, it should take a lot quicker.

(I have tried this method before with Steam and it has worked. Just be mindful it only works for Steam games on PC).
Hope this helps.

Credit to this YouTube video for the guide: https://youtu.be/wXFfn0yEAUM?si=nAoZzytEKOSQ0EVT