Organic water clean flux from Kester has a unique smell that I would consider annoying. Some of the lead free solders can be a bit off putting too, but then again I am very sensitive to smell. Regular old RA flux or no clean are my go to solders and I have no problems. At both our assembly stations at work and my bench at home I just have a small fan (I use a 4 inch 12V dc computer fan with a wire wound pot for speed control) to blow the smoke away and have no problems. Lab coats do make you feel more official though. As said before though, make sure you get one suitable for ESD, otherwise just plain old cotton clothes are way better.
On a side note at my last years physical I explained to my doctor all of the materials I encounter at work over the last 25 years and asked for suitable tests. Lead, heavy metals, etc. Apart form electronics I also spent some time before it got to expensive loading ammunition. I was sure it was going to come back as something somewhere and it turned out nothing out of the ordinary. Actually my mercury was lower than average because I don't eat fish. My doctor explained that most of the materials and chemicals i encounter are not in a "Bio Available" state. In other words, even if they were to enter the body in small amounts, there are no receptors for them and they are expelled through normal process. Its when they are in a molecule that will combine with something else in the body is when bad things happen or are in sufficient quantity that enough biochemical reactions to take place to really get somewhere. In other words holding and using lead solder where the lead is bound in a rather stable alloy of tin, and whatever else is in it is much safer than lets say a solid lead bullet stuck in your body constantly shedding lead oxide which is reactive and poisonous.
Also things like solvent based flux removers and such are a weird animal. In small amounts your body will metabolize them much like any other hydrocarbon. Alcohol for example. When sufficient amounts are adsorbed or ingested they can cause a whole range of problems, but casual contact say in the act of cleaning a circuit board is not an emergency. Just wear nitrite gloves whenever possible and avoid breathing the fumes as they can cause airway constriction and asthma. Of course old ether flux removers should be avoided for obvious reasons.