The paths around the boating lake are already used by cyclists. However, the path shown on the map parallel to my suggested path is narrow and in dangerously poor condition. My suggestion is to create an armoured grass path as shown. The path that heads North at one end should be extended to join it, and the old path removed. This is to improve safety at what is currently a blind junction.
It would be good to address the bridge at the western end of the suggested path, which has wheel-grabbing slots.