You don't need much "pushing" force to cut away material. The router does not remove material by pushing it on to a surface.
What happens is that you approach the router to the surface and the tips of the cutting bit remove thin slivers of the materias as they rotate. So what you do is move at small steps at different depths.
What you need to know is the torque that your router needs to resist while cutting. I.e as the material is removed a torsional moment (aka torque) develops. You'd need to be able to resist that. The maximum value should be greater to the maximum torque of the router.