Estimating the 3D hand articulation from a single color image is an important problem with applications in Augmented Reality (AR), Virtual Reality (VR), Human-Computer Interaction (HCI), and robotics. Apart from the absence of depth information, occlusions, articulation complexity, and the need for camera parameters knowledge pose additional challenges. In this work, we propose an optimization pipeline for estimating the 3D hand articulation from 2D keypoint input, which includes a keypoint alignment step and a fingertip loss to overcome the need to know or estimate the camera parameters. We evaluate our approach on the EgoDexter and Dexter+Object benchmarks to showcase that it performs competitively with the state-of-the-art, while also demonstrating its robustness when processing "in-the-wild" images without any prior camera knowledge. Our quantitative analysis highlights the sensitivity of the 2D keypoint estimation accuracy, despite the use of hand priors. Code is available at the project page https://cpantazop.github.io/HandRepo/