I guess you can use MeshView as you are using Legacy DOLFINx, and create a projection operator from the parent mesh to the sub mesh.
In DOLFINx, you could use dolfinx.fem.Expression (see for instance Implementation — FEniCSx tutorial) along with sub-meshes, as explained in
Plotting Partial Meshes - #4 by dokken
As interpolation operators in DOLFINx can be supplied with which cells to act on, you can identify which cells are connected to your boundary, and only interpolate over these.