Grasping deformable objects with varying stiffness remains a significant challenge in robotics. Estimating the local stiffness of a target object is important for determining an optimal grasp pose that enables stable pickup without damaging the object. This paper presents a probe-to-grasp manipulation framework for estimating the relative stiffness of objects using a passive soft-rigid two-finger hybrid gripper equipped with self-sensing pneumatic variable-stiffness joints. Each finger of the gripper consists of two rigid links connected by a soft pneumatic ring placed at the joint, enabling both compliant interaction and controllable joint stiffness via internal pressurization. By measuring the pressure inside the pneumatic ring, we can estimate the interaction force during contact. Building on this, we propose a practical probing strategy to infer relative object stiffness by correlating the estimated normal force with known gripper closing displacement. We validate the self-sensing model through stiffness characterization experiments across bending angles and pressure ranges, and demonstrate stiffness-aware probing-and-grasping in real-life applications: selecting grasp locations on fruits with spatially varying stiffness. The proposed system offers a minimal, low-cost sensing approach for stiffness-aware soft manipulation while retaining probing and grasping capability.