Jim and Marie Edwards, who rely on the service to help fund the waka for its otherwise educational purposes, fear the sediment in the river is increasing at an unsustainable rate.
"It's had it's day," Jim Edwards said of the river. "If anyone can offer me a better waterway I'd accept it."
The Clive, the old path of the Ngaruroro River, meanders across the alluvial Heretaunga Plains it once helped form.
Edwards, who's been on the river since 2000, regards it as one of the great wonders of Hawke's Bay. But choking mud is nothing new.
The waka was "stuck" on the river three times last year, including once when passengers had to be transferred to a support craft to be taken ashore.
Edwards said he was looking into a dormant proposal for a water course for non-powered craft, including rowing, in the upper reaches of the Ahuriri Estuary beyond Hawke's Bay Airport.
"We've got to look at it," he said.
"At least the waka won't be lying on its side at its mooring. The waka doesn't deserve that."
Hawke's Bay Regional Council group manager asset management Chris Dolley said the Clive River was dredged about every 10 years, at an estimated cost of $1 million each time.
The next dredging is scheduled and funded for the 2019-2020 financial year, but the council had funded the recent sediment removal around the waka berthing area as an interim response to the Edwards' concerns.
Napier City Council city development strategy manager Paulina Wilhelm said a water course in the upper reaches of the Ahuriri Estuary had been mooted in the past but it was not being considered at the moment.
"Through the Ahuriri Estuary and Coastal Edge Masterplan engagement process it was identified that many bird species, some of them endangered, do nest in the upper reaches of the estuary.
"The rowing boats passing by this area could have a negative environmental impact," she said.
"We will not be pursuing/supporting this activity in that location before a proper assessment of that area is done."
The waka is due to carry its first cruise liner passengers this season on November 24.