Should not be a problem - used the NYK (Nichiyu) brand mast reach in the states for the same purpose. Used 4.8 meter full free lift triple mast w/side shift. Loads were stacked two high (approx 600 mm high on 600 mm x 500 mm pallet.
Two areas of concern you need to check out closely:
1. Will all the container door opening heights be the same - they can vary & cause you issues if the lowered height of the mast or OHG is too high.
2. Compare the maximum break over angle (between front & rear tires at the lowest point of the reach truck to the maximum break over angle of dock plate at the lowest & highest point. To make certain the reach truck will not get hyng up when either entering or exiting the container. Most mast reach trucks have approx 75mm of underclearnance