The 41-year-old runs the Wildman charity in Auckland, Wellington and Christchurch, which brings men together to chat around a campfire.
"I met a guy a couple of weeks ago who wanted to learn how to talk because his mate had killed himself earlier in the year and he just wished he'd known what to say."
With the money raised on this trip, Mr Cope hopes to open other branches in four more cities.
But so far, Mr Cope has not raised as much as he would have liked.
He needs $24,000 by Friday and so far $2000 has been donated to the cause.
Donations can be made through the Spark My Potential programme, which will match dollar for dollar once $6000 has been raised.
If he doesn't reach the goal, then he doesn't get any of the pledged money, Mr Cope said.
Taking a fridge with him on his tour of the country was "as crazy as you can get".
The well-travelled appliance was a bit battered from the trip.
"I took him paddle-boarding and I've had kids skateboarding on him."
His journey started on November 4 and he had been hitchhiking in a "figure 8" path around the country. He and Steve were due to finish their trip on Friday night back in Wellington.