The missiles are often the thing that carries both the damage of a skill and the animations, so skills.txt isn't as important as Missiles.txt. In Missiles.txt, there are several fields for animations. I'd recommend using the
PhrozenKeep File Guides to get a better understanding of things, at least reviewing the guide for
Missiles.txt. If you don't like reading, then modding might not be for you.
"CelFile" field can be changed to remove part of the animation, but I don't know if deleting the entry would work, that isn't done in other parts of the file where missiles have no animation, so when you make a change it's fastest to read other parts of the file to see how changes were made in the past.
Also check the appended missiles columns of the row, since some of those are purely for adding extra graphics. I know deleting these will in some cases break the skill, but there are no-graphics options to fill in.
It's a good idea to test after each change or small set of changes, so you know what broke things.
When you run D2, a text file named something like "DebugLogYYY-MM-DD.txt" is created that might help you out. Jump to the line where D2 is reading missiles.txt, and if the next line has stuff like, "line XX, field Y is missing", then that's about as kind as D2 will ever be for telling you where someone made a mistake.