The first thing you want to do is turn on Edged Faces in the viewport so you can see all the polys outlined. Right click on "Perspective" in the top left corner of the viewport and click on "Edged Faces". In that same menu you also want to go to "Configure" and then in the new menu that pops up under the "Viewport Rendering Options" section enable "Shade Selected Faces" and hit ok.
Now you should be able to easily identify the polys you need to cut to get the vertex you want:
Before going any further, you'll need to expand the Editable Mesh modifer, select the Vertex sub-mode, select the surrounding verts of these polys, like so:
Then in the "Weld" section in the value box for "Selected" put in 0.1mm and hit the "Selected" button.
Any mesh you import will typically have most of its faces detached, which will screw up attempts to perform many modelling operations, so unifying a mesh (or sections of a mesh) is usually the first thing you need to do. You can weld the entire mesh, but you need to be careful doing this, since in some cases you may accidentally destroy needed geometry (like two overlapping faces that have their normals pointed in opposite directions for backface culling reasons, common in character models) or run into shading issues if you don't manually reassign all the smoothing groups afterwards.
Go to Customize -> Grid and Snap Settings and tick "Vertex" on the Snaps tab. You can press the S hotkey to enable and disable snapping, so now you will be able to snap to vertices (in some cases you may want to also temporarily enable Edge and Midpoint).
Now in Polygon sub-mode, under the "Edit Geometry" section enable the "Cut" tool:
Then with snaps enabled, click on the starting vert of your cut line, then snap to the end vert:
Click on the end vert and you should have a set of new polys and verts:
Right click a couple of times or manually hit the button to turn off the Cut tool. Note that Max is a bit flaky about this sort of thing, refusing to cut across polys that aren't coplanar, so sometimes doing it from the Top viewport is more reliable.
Now you should have the vert/s you need to match the walkmesh. Note that you'll probably want to load in the textures to make sure that you are not getting too much distortion. In some cases creating new polys like this will necessitate adjusting the UVs to fix such distortion. In this case it should be fine, but given the propensity for terrible unwraps in KOTOR you're bound to get some distortion eventually when doing this.