Actually you should activate the new legendary key.
In the Steam client, at the top menu, click Games, "Activate a Product on Steam...", put in your key, and it'll add it to your library.
So your DLC's should be registered as Legendary Edition in the library.
You saves shouldn't be a problem, but back them up for any case: C:\Users\[Your Name]\Documents\My Games\Skyrim
If you want to install them from disk, after you finish the Activation just put the DVD in your drive and:
- Log in to Steam and click on Library.
- Right-click on the game, select Delete local content, and confirm.
- Insert the disc into your computer.
- Close Steam (Steam > Exit).
- Press Windows Key + R to open Run
- In the Run window type:
- "C:\Program Files\Steam\Steam.exe" -install E: (32 bit operating system)---------OR "C:\Program Files (x86)\Steam\Steam.exe" -install E: (64 bit operating system)
- Replace E: with the CD/DVD drive you are installing from if is not correct.
Replace C:\Program Files\Steam if your Steam installation is not in the default location. - Press OK. Steam will launch and ask you to sign in if you do not have your password saved. Your installation should continue from the disc.