Don't worry, he won't die of hunger if their is food available.
Sorry to be the bringer of bad news - but that is not totally correct.
dehydration can cause a lizard to go off the food as moisture is needed for digestion along with heat. if there is no moisture - then the lizard will not eat - therefore the lizard will lose condition until it dies from malnutrition. How do i know this? I've rehabbed quite a few blueys on deaths door.
the baby could be settling in. they do go off food when relocated to new enclosure at times. If you maintain day time temps at around 30 - 32oC - and night time temps around 18 - 20oC the temps should be fine.
Feeding cat food is fine - but as stated - no fish. As is Dog food. Mince meat is a questionable one as I know of people that have had bad experiences feeding it - however I have also done so and had no problems. Roo meat is good. Scrambled egg is GOLD!!!!
Snails are also Awesome and so are pinkie rats/mice - however don't try feeding your little guy pinkies yet - wait atleast 6months and make the call depending on the blueys size.
In regards to the UV debate.
There is NO proof that UV is needed for blue tongue skinks. I persoanally keep most of my lot without UV with no problems - however I have also kept some with UV and also experienced no problems. if you are concerned about the UV issue - you can do a few things.
1, get a UV bulb. ( I personally shy away from this for one simple reason - COST. they cost far too much and do a bad job. Natural sunlight is better.
2, Take your bluey outside. (you can take your bluey out for 20mins a day - and will have no issues at all).
3, Suppliments. (You can suppliment the sunlight with calcium and D3 suppliments. Reptiles need the UV light so they can create Vitamin d3 which enables the animal to absorb calcium. However, due to modern marvels, we have suppliments that do everything the sun does. Reptical make a good calcium with D3 powder, and you can also add some herpivite for extra vitamins and minerals.
Suppliments are a more effective way of doing things of you lead a fairly busy life. If you leave for work early and arrive home after dark - you don't have to worry about UV light or taking them outside as you are supplimenting these with the powders.
(just want to state that yes i said that UV has never been proven to be needed. I'm talking specifically about Blueys. UV has been proven to be needed with other species - just not Tiliqua - so to use UV or suppliments is to do so to be safe rather than sorry)
So, make sure you have clean water in the enclosure, the temps sorted, and all the rest should follow in due time.
My guess, it's a relocation thing. try what herptrader said - He's right about the snails - especially with babies.
Snails are like Bluey heroin.
if after 2 weeks the bluey still isn't eating - then start to be concerned - but for now - relax and wait.