Once you have imported the mocap files into Softimage, you can constrain your rig to the mocap skeleton, then plot (bake) its mocap data to your rig. When you're plotting, you can choose to save the animation in an action source so that you can use the animation mixer, or simply create a library of sources — see Plotting (Baking) and Storing Mocap Data for more information.
You can constrain the skeleton and rig together in different ways, depending on which elements of your rig are IK and which are FK.
For IK elements, one common way is to pose-constrain the IK effectors, roots, and IK control objects (including up-vector controls) on your rig to the appropriate elements on the mocap skeleton's.
For FK elements, such as arms, you can orient-constrain your rig's bones to the mocap skeleton's bones. If the resulting orientation on your rig's bones is not correct, modifying their rotation order may help — see Changing the Bones' Order of Rotation.
For more information, see Constraints and Rigs.
Instead of constraining your rig to the mocap skeleton, you can also retarget the mocap data from one rig to another, and then plot (bake) the animation onto your rig — see Overview of Retargeting Animation with MOTOR for information.