The mortuary is a small building surrounded by trees and some distance from the rest of the hospital.
Although it has a security light on the building, the light doesn't work.
"It can be really unpleasant, especially on a stormy night, when someone could easily be hiding in the trees," Mrs Kenny said.
"It's pitch black here, and you'd never see or hear someone in the bushes."
She said the danger was compounded by having to undo three separate locks, plus an alarm, on the mortuary building.
"I have felt quite vulnerable at times."
She said she had raised the issue of safety several times with hospital management, but nothing had changed.
Just two weeks ago she had a meeting with police and hospital iwi to talk about safety.
She would like a holding room in the main hospital to safely keep patients who had died overnight.
"We don't want anything fancy, just a room where they can be kept until daylight, then transferred to the mortuary.
"I've asked about this many times, but nothing has been done." Mr Forrest said while he and Mrs Kenny had raised the issue for their staff's sake, there was also the issue of hospital staff safety.
"Sometimes hospital staff have to come down to the mortuary during the night, and it can be an unsafe situation for them as well."
Whanganui District Health Board member Ray Stevens has asked for the issue of safety on hospital grounds to be brought up at Friday's full board meeting.
"I want this discussed at a wider level, but I'd like these specific issues [raised by Mrs Kenny and Mr Forrest] to be raised as well."
The health board had a duty to ensure the safety of staff and any contractors on site, he said.
"It's sad that someone has to be hurt before something is done about this," Mr Stevens said.
Brian Walden, health board strategic and corporate general manager, said the mortuary was mostly used after hours by the police.
"We are confident the police would have raised concerns if they considered the area to be unsafe."
Mr Walden said hospital use of the mortuary after hours was "very rare".
"But when Wanganui's two funeral companies do need to access it, they can call the operator and request assistance from hospital security or an orderly. They usually choose to pick up the key directly from the telephonist."
"The safety of staff and contractors is paramount so we have listened carefully when staff have told us they believe the lighting levels around the Wanganui Hospital campus to be satisfactory.
"Any member of staff who has to cross the campus at night knows they can have security support," Mr Walden said.
-Despite repeated requests, Armourguard, the company which employs the injured security officer, has refused to comment to the Chronicle.