Existing bicycle connectivity would be compromised. Currently, bicycle riders can ride from the intersection of Spring Street and West Botany Street to Marsh Street, all away from major roads and mostly on bicycle paths. In the DA plans, bicycle connectivity starts from somewhere between Terry Street and Tantallon Avenue. For the section from Spring Street to that starting point, the plan says "Existing path to be retained & protected". That path is a footpath that does not go all the way to Spring St but is to be extended there with a width of 1.2m which is too narrow to be shared by bike riders and pedestrians. The diagram from the document "Appendix E - Public Domain Report and Plans Part 5 - Cook Cove Southern Precinct" shows how the bicycle path (in deep green) terminates at the footpath of West Botany Road. Clearly it is going to be difficult for bike riders to safely and legally enter or exit the bike path at West Botany Street.
The existing path also has a diagonal section from near the bend in Firmstone Garden to the start of the northern section of Eve Street. This section would be pushed towards the backyards of Firmstone Garden, making it longer and curvier. Apart from increasing travel time for both pedestrians and bicycle rider, this has safety implications because riders coming from the north would enter the first curve after a downhill section where they can be expected to be significantly faster than usual. There is a curve there now but that curve will have an increased angle. Existing visibility issues would become worse. The diagram is from "Appendix E - Public Domain Report and Plans Part 6 - Cook Cove Southern Precinct" and shows that section of the new bicycle path (red annotations from me).
Elsewhere the destruction of old shared paths and the construction of new shared paths more or less cancel each other out.
According to the NSW government document Cook Cove Indicative Development Proposal - Kogarah Golf Course Relocation, There is a bicycle path planned along the foreshore on the site of the current golf course. Such a path would improve connectivity between the city and Kyeemagh. However, this section need not be contingent on sacrificing Cooks Cove South as explained in the New Amenitities section.