Your refusal to vaccinate your child put many people at various types of risk. First, not everyone is able to get vaccinated. Some people have allergies to the ingredients or have weakened immune systems. By not vaccinating everyone who is able, the likelihood of an outbreak increases, which increases the risk to these people.
Second, depending on when you were vaccinated, the vaccine had different rates of effectiveness. In the 60s, when the vaccine was new (and different than the current one), the efficacy was only about 92%. That means that for our parents/grandparents, 8 out of every 100 people do not have immunity to the measles. Even today, the efficacy is 98-99%, which is incredible, but not perfect. If everyone in your kid's school was vaccinated, and 98% of them had immunity, there would be no outbreak in your school because the virus wouldn't be able to spread. By not vaccinating your kid, you're increasing the number of people who don't have immunity, which increases the likelihood of an outbreak, which increases the risk for those who either could not be vaccinated or are unlucky enough for the vaccine to have not been effective.
Third, there is more than one type of risk. My risk of getting sick might be very low, but your kid's is much higher. If your kid gets sick, they're going to require treatment. Your insurance will cover that treatment, but the insurance company will likely lose money over it. If enough people get the measles and the insurance companies lose money over it, all of our rates are going to increase.
Along the same lines, I think you underestimate the severity of the measles. Like you said, it certainly isn't a death sentence, but complications are fairly common. About 10% of children with measles will have an ear infection that can lead to hearing loss. Just under 10% will experience diarrhea, which when combined with the other measles symptoms can require hospitalization. About 5% will get pnuemonia, which will require hospitalization. 0.1% will suffer encephalitis which will require hospitalization and can cause mental retardation and deafness. And yes, 0.1% will die.
Now, frankly, your child dying doesn't peronally affect me much, but your child being hospitalized certainly might. First, like I said before, hospitalization costs money, which affects all of our insurance rates. Second, a measles outbreak places a burden on a hospital that will affect the resources available to others. Third, many people in a hospital are already sick and have weakened immune systems. Exposing these people to your sick kid puts them at risk for infection.
So yes, your refusal to vaccinate your child puts others at risk.