The fastest way to switch skills in Diablo 2 is to use the mouse wheel or direction function key. In order to do this, you have to assign skills to your F keys and then you'll be able to switch to them in order of what you have assigned.
- Open up your quick list of spells (default S key)
- Hover over the skill you want to assign with your mouse to F1 and click F1
- This will have now assigned the skill to your F1 key
- Continue to do this for any number of skills you want to do
- Now you have the option to actually press the function key to jump straight to the skill or use the mouse wheel to cycle through your skills in order
Alternatively, with Diablo 2: Resurrected, since Patch 2.3, you can activate "Quick Cast" from the game options, which enables the activating of the spell/ability on function button press immediately, without to need to click left/right mouse button (default button)