I always take wheels with us when we travel with the hedgehogs. They can take up some space in the "luggage" but I always just pack cage liners, wash clothes and wrapped food bowls, etc inside the wheel and around it.
I figure the hedgehog is less likely to try to escape their cage or totally trash it (spilling water, etc) if they have their normal source of entertainment (running for hours on their wheel). Or scratch at the side of their cage.... I know what the sound of the scratching Inky made... I'd rather have clinking of glass water and food bowls
