Force-sensitive manipulation requires contact and load information that is not provided explicitly by visual observations. We present CW-WAM, a world action model that jointly predicts video, motion, and contact wrench. Inspired by hybrid motion-force control, it contains a unified interaction module that treats both motion and contact wrench as modeling targets and predicts time-aligned motion-wrench chunks as control references. A pair-causal attention mechanism structures the motion-wrench dependencies, while a long fixed-length wrench memory retains past interaction information. The predicted wrench chunk acts as a force reference for a 20-Hz outer-loop admittance controller within a slow-fast control system that maintains force feedback and smooth motion between model queries. CW-WAM improves contact prediction and increases the insertion success rate from 25% to 70% for square pegs with 1-mm clearance per side and from 40% to 95% for power adapters, compared with WAM without wrench input. It also improves lifting-height accuracy across different loads. Our framework with an admittance controller reduces force-reference RMSE from 4.8 to 2.7 N for peg insertion and from 2.0 to 1.3 N for wiping, respectively, with smaller force fluctuations during successful execution. Project website: https://cw-wam-project.github.io/