What is the probability of squamous cell skin cancer spreading to lymph nodes?

Rare but happens: While basal cell skin cancers almost never metastasize to lymph nodes, squamous cell cancers do, but rarely.

It depends: The odds of scc spreading depends on many factors such as how well-differentiated the cancer is (well-diff spreads less than poorly-diff), how large it is(larger more likely to spread than smaller) and other factors such as the health of the patient (immunosuppression leads to spread) and locations (some body sites worse than other). If you're young, healthy and it's small, odds are low.