If you injected a tumor with epithelial cells infected with the Rhinovirus, would this still evoke an immune response as it would with the respiratory system? Secondly, what is the specific reason the Rhinovirus is only attracted to the epithelial cells in the respiratory system. Do these cells give off a specific chemical signature in which the virus is attracted to?
Infecting tumor cells with viruses to provoke an immune response used to be termed (tumor / immune ) 'xenogenization'. The approach may now fall under the general headings of tumor immunology, immune modifiers or tumor vaccines. Xenogenization been explored for decades (with only moderate success). Some modern approaches include adding immune stimulating genes to the viral 'vector' (e.g GM-CSF) to try and improve an immune response. Xenogenization is usually intended for use with the patients own (autologous) tumor cells. Other approaches that use viruses include delivering genes that preferentially act in tumor cells or "tumor antigens". Some of these modified viruses may have been engineered to have low, or no, ability to replicate in the body. Note that some viruses, such as influenza or rhinoviruses are not (generally) able to circulate in the bloodstream (viremia) to infect distant tumor cells. Instead, the goal of using such viruses is to provoke an immune response against tumor antigens expressed on the 'original infected' cells at the site of injection and hope that the immune system goes on to attack distant masses/metastases.
The virus has some molecules on it surface, which fit to receptors on the surface of their host cells. In the case of rhinoviruses there are three receptors possible. The viruses of the so called major group (or HRV-A species) dock to ICAM1, the minor group (or HRV-B species) to the LDLR (low density lipid receptor), and the relatively recent group of HRV-C dock to the HRVC receptor. See the image below. It is taken from this article ("Human Rhinoviruses"), which give a pretty nice overview of the field.
Regarding the injection question: You will provoke an immune reactions against the epithelial cells, if the are from a different person. If they are not, these cells will simply die and nothing else will happen.