Do you mean 40cm deep? Ideally the minimum recommended size is about 70cm by 40cm. The Duna Fun is way too small. This is the Duna Fun Large which just meets the minimum, but is a bit on the small side for a hammy really. It's the same size as the standard duna multy, so the base should fit. Although it says 46cm deep, that is at the widest part so it'll probably be about 40cm deep at the base.
Ferplast Duna Fun Large Hamster Cage
I'm not sure there are many cages that are only 40cm deep as 80cm by 50cm is seen as the ideal minimum usually, but a bit of overhang at the front should be ok
There are probably better cages you could get for less money. The Hamster Heaven is less than £60 at Zooplus and is a good sized cage and not too high. Although it's 50 cm deep, again that is maximum measurements - but if it sticks out 10cm at the front it's balanced/heavy enough that it would be fine.
Savic Hamster Heaven Metro Cage | Great deals at zooplus!
Or you could get a standard Duna Multy for about £33. It's basically the same as the Duna Fun large but without the extra bar bit and the extra height.
Cage Duna Multy
A great option for a dwarf hammy would be the Maxi Duna Multy - it has a deep base for lots of substrate for digging and burrowing, narrow bar spacing on top and plenty of floor space so you could make different levels have lots of hidey places and tubes etc. Like all the others it's deeper than 40cm but a big of overhang at the front should be ok or even a bit at the sides as well. The extra floor space (ie length) is much better than extra height as they use up so much energy.
Cage Maxi Duna Multy
Here are some examples of dwarf hamster set ups in the maxi duna multy (it's big enough to fit a labyrinth house which can double up as a shelf/level).
https://www.google.co.uk/search?q=ma...CEA8oQ_AUIBygC
Maxi Duna Multy Has Arrived!
http://www.hamstercentral.com/commun...8-post144.html
Obi's natural set up is complete!
Or - if you don't mind a bit of diy you could make a bin cage. Some of the bins are longer and narrower, but it doesn't always work out much cheaper.
One thing that would fit depthwise is the detolf
- but it is quite long so you probably wouldn't have room for it.
163cm long by about 42cm deep. It's a glass tank from Ikea you tip on its side and leave the door off, then make a lid for it from wood and mesh.
https://www.google.co.uk/search?q=ma...hamster+detolf
I did a video recently on my top 10 favourite hamster cages if that helps - linked it below. Personally I would go with the maxi duna multy for a dwarf hammy. It might not look as much fun as the duna "fun" but you can make it look fun quite easily as you can see from the sample set ups above
https://www.youtube.com/watch?v=JSKzn0g3sVk