Here are my recommendations based on what I can see.
The biggest health risks are respiratory infections, intestinal infections, and tooth problems. Your vet has pretty much ruled these out. Your biggest indicator of problems is going to be trends in weight. Weigh your chin once a week and look for sharp weight loss trends. Of course fecal output is a big indicator as well. Make sure there is no change in the texture or size either larger or smaller. Of course there are indicators like fur chewing, drooling, mucus from the eyes, etc. keep track of input and output and you may catch something before it gets that far.
Of course you know that one wrong move with the cat it's probably going to be over for your chinchilla. Cats are much tougher than chins.
-Cage (no useable information) Should be all metal with no plastic parts. All chinchilla cages should have solid pine shelving installed. If you need to modify your cage I can help you there with ideas.
-Snak shak (looked it up) I don't recommend this. It has honey in it and sugars are not good for chinchillas. Recommend wood huts made of solid wood.
-Chinnie Bedding (no indication of what kind). I'm assuming you're not using fleece lining. Do not use paper bedding or cedar chips both are dangerous and paper bedding is known to cause skin problems and bowel obstructions. Use kiln-dried white pine. For one chinchilla you should only have to change the bedding once a week to 10 days. Or unless you think it's starting to smell which it shouldn't until closer to 7-10 days.
-Diet (no indication of what kind). Please be more specific on this. There are many brands. The most expensive isn't necessarily the best. Chins should be put on plain alfalfa pellets. Mixtures are not good. Foods with fruits, nuts, or seeds are detrimental to them. You'd be amazed that good diets can be right next to horrendous diets known to kill pets on the same shelf.
-Hay manger (no indication). If it's one of those wire hay balls stop using it. Most designs of these are not safe.
-Dandelion drops. I recommend not feeding these. They have extra vitamins in them and they are sugary. Not really a good combination.
-Raisins. There's some controversy on these because they can harbor toxic mold that is known to kill them instantly although it very rare. I would recommend rose hips, and only one small one a day for an healthy adult chinchilla that is not stressed. Honestly I don't see a need for giving chinchillas treats as food. When you learn to interact with them you'll find they like to be scratched and they'll groom your hair and face. Your chin will eventually get used to being handled. If you need treats as a training aid to tame a difficult animal that is one thing but there is much less risk if you simply keep them on a regular diet of loose hay and quality alfalfa-based pellets. They simply do not need anything besides that to live very long lives.
I know I sound like I'm minimalist and boring but when it comes to chinchilla digestion you don't want things to get interesting. The safest alternatives are non-food treats and giving them personal interaction. You'd be surprised how they might interact with chew toys if you hold them in your hands.
Of course if you have any more questions or comments ask away. We have a good community here.
Okay so... I apologize for such limited information, I am so new to this lol *facepalm*
1.) the cage is all metal, no plastic. I bought one specifically designed for chinnies so it's well-established.
2.) Snak Shak - okay, I will be sure to research that again. I heard a lot of great things about it, so I will see what else I can find. I will take it out for now.
3.) Bedding - it is definitely not paper or cedar. I heard the same comments about both of those. It is a "wood" bedding for sure, dark brown. Soft and crumbly. I will double check once I am home.
4.) Diet - by pellets, I meant alfalfa pellets (-: That is all he is getting for now except those Dandelion Drops, 1 twice a week. Which leads to 5.) I will be sure to cut those out! He is gonna be mad LOL
6.) In regards to the cat ... he is very very old, I can only hope he is too arthritic and decrepit to do much lol I just hate to keep them apart, it seems to really worry the chinnie :-/ Perhaps a second chinnie would be better? I hear they enjoy company if they are coherent with one another.