What's the meaning of "Wanted on Voyage"?

Solution 1:

When people travelled long distances by ship, they sent their bags to the ship in advance, or checked their bags dockside. Those were the days when people travelled with enormous amounts of luggage, partly because they took long trips and partly because their clothes were more elaborate.

Some of their bags would be delivered to their stateroom, but most of the bags would be put in the hold of the ship. The latter were labelled "Not Wanted on the Voyage"; the former were tagged with the stateroom number. I don't think they were also labeled "Wanted on the Voyage", but I am not sure. But they were understood to be Wanted on the Voyage.

Source: Personal knowledge from childhood trip, reading English novels, and this. Also, thanks to @AndyT, the National Museums, Liverpool.

Solution 2:

'Wanted on voyage' means that Paddington wants the suitcase as hand luggage on the voyage, rather than it being hold luggage.

Hold luggage:

Checked baggage refers to the items of luggage delivered to an airline or train for transportation in the hold of an aircraft or baggage car of a passenger train, which means it is inaccessible to the passenger during the flight or ride. - Wikipedia

compared with hand luggage,

Suitcases and bags of a size suitable for carrying on to an aircraft. - Oxford Dictionary

Which is accessable during the voyage.

The reason for this is that it contains a large jar of marmalade, which he eats throughout the journey.

“But whatever did you do for food?” asked Mr Brown. “You must be starving.” Bending down, the bear unlocked the suitcase with a small key, which it also had round its neck, and brought out an almost empty glass jar. “I ate marmalade,” he said, rather proudly. “Bears like marmalade. And I lived in a lifeboat.” - Paddington extract (pdf)

Since the marmalade was in the suitcase, and he was not a legitimate passenger, he needed the suitcase near him during the voyage.