Where I live, in trendy Norf London, far from being seen as nerdy, cycling is very much The Done Thing. Most of my (male) contemporaries cycle the seven or eight miles into town every day. I've never heard anyone bemoan it as being dangerous. I must admit I do miss my showers (the place I go is being refurbished) but fortunately we have a sink in the office, so I just strip off and go for it with an old t-shirt. No complaints so far...
As to answering objections: "I had a full health & fitness checkup recently, and was told my levels of fitness 'would be unusually good in a 20 year old'. I'm 49."