Interesting Dispel Magic Questions

[RSP]

The only is the sticking point, "Self" does not mean it targets only you, it does mean that it does target you.

“Self” absolutely only targets the caster, per the RAW. Again, it’s a rule oft broken, but that is very much the rule:

“Range
The target of a spell must be within the spell’s range. For a spell like magic missile, the target is a creature. For a spell like fireball, the target is the point in space where the ball of fire erupts.

Most spells have ranges expressed in feet. Some spells can target only a creature (including you) that you touch. Other spells, such as the shield spell, affect only you. These spells have a range of self.”

You're focusing on semantics. What was the intent of the Dispel Magic? Was it specifically to end the Shadow Blade? Then it's done and don't get rules lawyerly on whether the caster said he casts it on the character or the sword. Was it cast as a generic debuff to dispel whatever magic buff the character had? If Shadow Blade was the only spell in effect then it's dispelled and don't get rules lawyerly on whether the caster said he casts it on the character or the sword. If the character had Shadow Blade and another buff spell on him, Bless, Protection From Energy, Aid, whatever buff spell you can think of, even having more than one buff spell by a million different spellcasters, since in this example the caster wasn't specific as to which spell he wanted to dispel just dispel something, then randomly choose which buff spell is dispelled which may or may not be Shadow Blade as the final choice and don't get rules lawyerly on whether the caster said he casts it on the character or the sword.

Has nothing to do with being “rules lawyer”. DM dispels (or attempts to dispels) everything on its target. You can house rule it to be “pick just one spell” but RAW, what you’re targeting matters.

That’s why the question is important: if the DM targets the SB, SB is gone, but no other spells on the character are affected. Whereas if the character is targeted, the object SB may be unaffected.