There would not be.

Example:

Stand on a scale and put a cup of water at your feet.

Tie a string around a rock and hold it.

Note the weight.

Allow the rock to dip into the water.

The scale will remain unchanged.

Negative bouyancy only means than an object will sink if not suspended. It is not an added force that needs to be considered, especially considering that the steel ball is externally supported and negative bouyancy can not apply as a result.