If I have unhandled exception in Java, Eclipse proposes two options to me: (1) add throws declaration and (2) surround with try/catch.
If I choose (2) it adds a code
Personally, I use a generic idiom irrespective of the actual checked exception type, you might make Eclipse use that as a template instead:
try {
...
}
catch (RuntimeException e) { throw e; }
catch (Exception e) { throw new RuntimeException(e); }
The point is to wrap the whole code block instead of individually each line that may throw an exception. The block may throw any number of checked and unchecked exceptions, and this will allow the unchecked exceptions to pass through unharmed, and the checked exceptions will be wrapped.