Yep, I would definitely start asking the oncologist about chemotherapy options - from some quick reading, it appears that many SCC tumors have an excess of EGFR protein and there's a drug which targets this.

Below I'm linking a related research study to share with your oncologist. Note that the patients were in a much worse situation than you are. They couldn't have surgery to remove the SCC tumor and relied on the chemo alone - and a third of them were immunocompromised. You just need to keep any remaining cells from regrowing.