Put out ashtrays for those who smoke if you want. Chill out and have a good time. Don't wear your underwear so tight. Hang out with people like Jesus did. Dismantle any holy huddles that don't result in loving, grateful service to God.
Relationships are the key.
You will only reach these men if committed men in the church take the time to invite them. They will almost never come on their own initiative. Don't expect to just host an event and reach men on the fringe. If they don't get personally invited, they won't come. Communicate the vision so men in your church are excited about the opportunity to invite other men.