No, washing your hands isn't enough.
There are numerous cases every year of people/children contracting Salmonella from their pets.
It is shed through fecal material. You need to be extra careful when you are cleaning cages, bowls and anything else that goes in or out of the cage.
And just because it hasn't happened yet, doesn't mean it won't. Salmonella is shed intermittently. That means the animal can have the bacteria and not shed it for weeks/months/years at a time. So it's impossible to accurately test for the disease. You should ASSUME that every reptile is a carrier and act appropriately.
One common scenario is someone cleaning the animal's
food bowls in the sink, and then NOT sterilizing the sink area. When
human food utensils/bowls/plates are "cleaned" there, they become contaminated. This happened with the bottles of an infant in one case, and the infant died.
Reptiles should not be kept in households with small children or immune suppressed individuals. You're risking someone's life if you do. Sure it's a small risk, but the life of a child is worth more than what can sometimes just be the selfish gratification of having a lizard or a snake. If it's your job or livelihood, that's one thing, but if it's just an indulgence, that's something else altogether.
So there are other ways to get it, if you think just washing your hands is enough, you're wrong. You have to be careful about everything, and small children should never handle it or anything that's been in contact with it.