I researched the city ordinance carefully, and the definitions in the no discharge clause refers to firearms. I spoke to two officers that agreed, but said that if a neighbor complained they would be obligated to respond and talk to me anyway.
I've spoken to all my neighbors in line of sight and obtained permission/made sure they weren't uncomfortable with it. Two of them that I hadn't previously met turned out to be bowhunters.
Still, I try to shoot early in the morning when there's less chance of anyone noticing...