Reaching-and-grasping is a fundamental skill for robotic manipulation, but existing methods usually train models on a specific gripper and cannot be reused on another gripper without retraining. In this paper, we propose a novel method that can learn a unified policy model that can be easily transferred to different dexterous grippers. Our method consists of two stages: a gripper-agnostic policy model that predicts the displacements of predefined key points on the gripper, and a gripper specific adaptation model that translates these displacements into adjustments for controlling the grippers' joints. The gripper state and interactions with objects are captured at the finger level using robust geometric representations, integrated with a transformer-based network to address variations in gripper morphology and geometry. In the experimental part, we evaluate our method on several dexterous grippers and objects of diverse shapes, and the result shows that our method significantly outperforms the baseline methods. Pioneering the transfer of grasp policies across different dexterous grippers, our method effectively demonstrates its potential for learning generalizable and transferable manipulation skills for various robotic hands