Skip field with __get_pydantic_json_schema__

[pigexperiment]

Is it possible to implement something similar to SkipJsonSchema through __get_pydantic_json_schema__?

I want to use custom schema generators, along with context variables, to modify the json schema.
One such use would to skip fields in the json schema depending on the context.

I see that SkipJsonSchema simply raises a PydanticOmit error, but when I raise it in custom types, the exception isn't handled, and it does not work.
Is this a bug? If not is there some other way to achieve what I am after?

I am using pydantic 2.7.1