We had an external freezer container. It was placed in a trailer well so we had it blocked up on one end to be level. We placed some external pest traps around it. That being said, I think the risk is pretty low because a mouse would have to have jaws of steel (note: they have strong jaws but they're not supermouse) to bite through the side of the freezer shipping container, which is reinforced and insulated. Additionally, the food inside is frozen. It's not likely to be much of an attractant. And a mouse certainly isn't going to be trying to sneak inside the freezer (ours was maintained at 0°F) to cool down or something.
Now your external ambient container may be another matter. I'm not entirely sure what gaps you have but I would certainly cover them as your pest control provider suggests and consider some additional traps.