I’m not sure to what degree dogs and other animals SMELL fear, although there is some evidence that we do make fear-stink. But it would be entirely beside the point, because when your body language is absolutely SCREAMING fear-signals then the scent to back it up would be superfluous.
With predator animals, you don’t necessarily want to send off prey signals like running away, but that’s not generally what is happening with dogs, cats, and domestic pets - they know you’re not prey, although some small children may trigger the prey instinct. The issue is the opposite, if anything - you are large enough to pose a physical threat, and if you present yourself as a threat then the animal may react as such. A larger animal being fearful and agitated - or a young animal guarded by a large parent - is a very serious potential threat, especially if the dog has any experience with people hurting it. I have a rescue dog that is extremely fear-aggressive due to neglect and abuse, and it makes a dramatic difference what signals people send. When you see a dog and start acting visibly afraid, the dog becomes alarmed and reacts.
A dog doesn’t understand why you are afraid of it, but it does immediately recognize that it has just met somebody who is reacting to it as if there is a conflict situation. If a dog has overwhelmingly positive experiences with people, it may react to this with mild confusion or just assume you need to be shown that it’s a friendly dog who you should feed and pet. If it’s a dog like my rescue dog, on the other hand, you have just sent it the signal that something is wrong and that it may result in pain and anger, causing the dog to react with fear, barking, and/or aggression.
So you definitely want to teach your kids that animals can SENSE fear and that it’s almost never a good message to send. If you don’t like dogs, then what you want to project is a lack of interest and just wait for them to pass. If a dog lunges at you in way that allows it to bite you, your best response is to stick your knee out in to it’s chest, which blocks off the attack. You should never approach any animal that is showing signs of fear or aggression, even if you like animals. If you don’t want an encounter, then calmly move away. If you want to see if it is friendly, then assume a non-threatening posture and see if the animal decides to approach you. Note that wagging tails can be a stress indicator and do not necessarily indicate friendliness. Also note that bending over an animal or moving your hand towards the top of an animal’s head is perceived as a threatening gesture by just about every species of animal in the world. I see this all the time… imagine how you might react if something many times your size leaned down over you and tried to swipe at your face with it’s enormous hand? It amazes me how many people don’t understand this and end up getting bit or scratched as a result.
So yeah… unless the animal is blind, whether they can SMELL your fear is the least of your problems. It’s your body language that you need to control. 