It's a fiendishly difficult topic, as I've said. It's only relatively recently that serious and long term studies have been done to determine potential sea level rises, and we still have no clear idea of how things will pan out over the longer term,
To illustrate the difficulties involved, this is an abstract from an academic site regarding the geological problems involved in determining potential sea level rise:
"The errors involved in attempting to correlate evidence of sea-level change gathered from disparate areas are discussed as follows:- 1. Errors due to levelling, especially in deep boreholes and at sea. 2. Problems of identifying the horizon to be levelled, and uncertainties that this horizon does represent the intended relationship to water-table. 3. Uncertainties in relating recognised changes in water-table, as indicated by vegetation or sediments to sea-level. 4. Errors in the estimation of present-day tidal levels, particularly in areas with a large tidal range. 5. Variations in tidal levels over time, especially in areas such as the English Channel and estuaries, where large changes in the coastline may have occurred. 6. The importance of the rare event, e.g. storm surges; and astronomical causes of variations in tidal levels. 7. Consolidation of sediments as a result of gravitational compaction. 8. Changes in the relationship of vegetation zones to sea-level, during periods of rapid sea-level rise. 9. Variations in the closeness of correspondence between sedimentation rates and sea-level rise. 10. Errors in radiocarbon dating. All the available ‘sea-level’ radiocarbon dates for Wales, S.W. England and the Channel Islands are plotted on the same diagram, as error ellipses. No significant difference in sea-level rise is apparent between S.W. England and Cardigan Bay. Only in the case of N. Wales is there a strong suggestion that isostatic uplift has had an appreciable effect in the last 8000 years. Important differences result from the use of M.H.W.S.T. or M.H.W.O.T. as the datum level. Any oscillations in the course of sea-level rise are smaller than the other uncertainties. No evidence of sea-levels higher than the present is seen."
The total amount of shipping tonnage world wide is estimated to be 186,000,000 tons while the total amount of oceanic water is estimated to be 350,000,000,000,000,000 tons, so to simplify that it amounts to less than 2 tons of shipping per 350 billion tons of water, which I'm reliably informed would amount to a displacement of around 0.0002 cm.
There are, however, lots of other factors, and the Pacific tectonic structure is far from stable, so uplifts do occur, sometimes with devastating results.
A holistic appreciation and study of the issue is mind-bogglingly complex, and I don't believe the Newspapers seeking to increase circulation and spark some panic is the best way to address the problem. More worrying is the fact that for some time the Earth's magnetic field has been changing; the magnetic North pole is now somewhere in Siberia.