That's an interesting idea. I don't see why that would be unsafe if it is something he merely licks off.
In fact I tried a similar thing with willow sticks that my chinchilla would chew and eat quite passionately. In fact I had to be careful not to give him too many because he would eat that instead of his food. I dipped the stick in the yogurt but he would have absolutely nothing to do with it. I tried a spoon, my finger, and even putting some on a raisin. I also put some on a spoon and set it in the cage. He did eat raisins and willow sticks without the yogurt though.
In this particular case I gave up on yogurt and went with supplementing with calf manna. The calf manna helped to stabilize his weight but eventually he wouldn't eat enough food for his digestive tract to function and then stopped eating entirely. He was diagnosed with malocclusion and promptly euthanized. He had lost over 20% of his weight and was starting to show it.
My new chinchilla doesn't like yogurt either but because he is new it might not be the best time to try it. I loaded some into a feeding syringe and dispensed a drop on the tip and tried to get him to lick it off. He just doesn't like it so I won't force it. It turns out that typically chinchillas won't accept yogurt. Turns out he really didn't need it. On his regular diet he is gaining about 2 grams per day.
