Unlike the other primary races, in which parties select their candidates for the general election, in this race the winner is immediately seated to finish the remainder of Green's term, which expires in January 2016.
Wolfe is taking time from his law practice to practice what he preaches - civic involvement. Campaigning costs him time and time is money.
"I'm in solo practice," he says. "I eat what I kill."
Wolfe doesn't smile easily. His mien is somber, reminding me of Mr. Burns, Homer Simpson's boss. "I'm not a likable guy," he says, but he's kidding. I think.
We'll get to the issues in a minute, but first the politics.
The reason he'll need magic to win is the almost 7-to-1 registration edge Philly Democrats enjoy.
What Wolfe sees in his favor:
* Low turnout for primary elections. The smaller the pool of voters, the better Republican chances - if the GOP can muster its outnumbered troops.
* Democratic apathy. Democratic gubernatorial candidate Tom Wolf is so far ahead that it may depress turnout by supporters of candidates Allyson Schwartz, Rob McCord and Katie McGinty.
* Name recognition. Wolfe tells me "at least 100 people" told him they love his TV ads. Those ads are actually for Tom Wolf. "I'm thinking of growing a scraggly gray beard to complete the illusion," Wolfe jokes over coffee in Center City.
What does it say when a candidate is happy voters mistake him for someone else?
I've known Wolfe a few years, starting when he emerged as a leader of the insurgents who staged a palace revolt against the GOP Old Guard that went along to get along with Democrats to glom a few patronage jobs.
The Young Turks won and when Green decided to leave Council, Wolfe "saw an opportunity." He has never before run for public office.
I ask Wolfe about his platform. His Big Ideas sound like conservative boilerplate - cutting taxes and spending, imposing term limits, forcing elected officials to resign to run for another post.
As for the last, he says allowing candidates to keep one job while running for another concentrates political power in the hands of the "haves." He may be right, but is this or term limits a hot issue?
More cogent is Wolfe's opinion that city government has, basically, four "core" functions: Fire, police, sanitation and education. That's it.
"If they canceled everything else the taxpayer would be happy," he believes.
Health and welfare should be a state responsibility, he insists, ignoring the reality that our Republican-dominated state government equates such spending as catching MERS.
When I ask him what specific program he would drop, it's economic development, saying lower taxes would spur development.
Just $28 million goes to economic development in the city's $4.5 billion budget. Not included in Wolfe's "core" are public health, libraries, museums, commerce, parks and recreation, housing, arts, culture and more.
With his idea of city-as-skeleton, Wolfe will need Merlin to win.
On Twitter: @StuBykofsky