Should I worry about getting skin cancer from drying my gel nails under a led light @ the nail salon every 2 weeks? Is led light safer than the uv?

No. Led lights have no affiliation with skin cancer however uv does. In fact uv light causes mutations in dna of skin cells, which causes excess proliferation of those cells or cancer.
Led is safe . Led or light emitting diodes have no risk of damaging skin. This low level light is used to reduce inflammation and help skin. You should be more concerned about the gel for your nails , make sure it's a product made in the usa as some foreign made products have different quality standards.