I like labyrinth houses but they’re not necessary. A shoebox house is just as good. Or something big enough for them to build a huge nest and have a litter tray inside in one corner. Putting the old cage base (without the cage top) into the new one is also an option. It does mean some rearrangement of the cage when you remove the old base a couple of days later. I prefer the adjustment day
. If space is an issue the hamster could be introduced to the new cage in a different room maybe. Then when moving him over have the new cage in the main room and take the other one away so you‘s only ever have one cage in the room.