Check if a value exists or catch an exception
I would recommend that you use option 2, especially since you have the ability to avoid the exception (by using the has method).

Exceptions should be used in exceptional circumstances (e.g. You might expect getInt to throw an exception if J_ID_CHUNK_TOTAL exists but does not contain a character which can be parsed to an integer). In which case you would want to wrap the call to that in a catch.

I would also suggest that you do a null check against the jUpdate object before using it.