During the years I served in very inner-city Boston I did a whole lot of street evangelism (called it that, too!) and it wasn't Bible-brandishing, sin-convicting and hellfire-threatening in style or substance; I was about getting people at least to talk about something, about anything, and then to get them into some church-related activities, eventually to Worship, Word and Sacraments.
Here's a story related to that time:
When I was on staff there, we had a new church musician who was a recent graduate of the evangelical Wheaton College in Illinois (as opposed to the secular Wheaton College that's in Norton, Massachusetts). One day this particular young woman approached me and said, "I need to talk to you! This isn't very evangelical!!!!!" But by my standards our proclamation and service to the congregants and to the community was extremely evangelical; her expectations seemed to be tent meeting/circuit rider!