There have been some problems with erosion on the beach, so there is a new access "Cape Point Bypass Extention" for of road vehicles, behind the dune line. Not sure if this would be a shorter pedestrian route. Here is a link to the news release.
Check the Facebook page for CapeHatterasNS for the latest ramp status
If it were me...I'd park at the end of lighthouse road, at the fish cleaning station, and walk out ramp 44 to the beach and then walk on the wet sand to the point. The new 'road' behind the dunes is deep soft sand...not walker friendly (IMHO).
I've never walked the entire way (I drive to the point) however a few summers ago we walked from the temporary closure, south of ramp 44, to the point (in knee deep water to comply with the resource closure 'rule' .