My recommendation would be to do this in ANSYS Meshing. Read up on body decomposition and multibody parts in ANSYS.

If I were to create it, I would create several bodies for the inlet tube network (I don't think they are all connected are they? I think I see three independent paths.) and then a mutli-body part for the thin air channel. You could create this in such a way that you would not have to go back and remesh when you are in a different position from the nominal. Instead, you would simply scale the mesh to adjust the dimensions. The downside to this approach is, you would not have a congruent mesh (1:1) at the tube/channel interface, but you could use a finer mesh to have the interface approach be effective.