when 싫은데? is said alone, instead of dislike/hate, does it mean "don't want to"?
As the question says, when a person responds 싫은데? to someone saying something like [Please stop.], Instead of it being a question or meaning that they dislike or hate it, does it mean more like they dislike the idea of doing that so...

싫은데? = I don't want to [stop].

Question

when 싫은데? is said alone, instead of dislike/hate, does it mean "don't want to"?
As the question says, when a person responds 싫은데? to someone saying something like [Please stop.], Instead of it being a question or meaning that they dislike or hate it, does it mean more like they dislike the idea of doing that so...

싫은데? =  I don't want to [stop].

Answer

Yes, you're right.  싫은데? in that context means exactly that.

You can think of it as (그렇게 하기) 싫은데? (I don't want to do that).

The "?" at the end also plays an interesting role.
Without it (or if written as 싫은데 ...) it might sound like "Um, I don't feel like doing that, but ...",  just wanting to avoid it.

Adding the question mark makes it defiant, like "I don't want to do that. So? What are you going to do about it?".