If you're knitting a shawl then I assume it's knitted flat, back and forth, not in the round. If so, as long as the stitches fit comfortably on the needle for you then you can just use whatever length you want. If you want to switch to a longer cable then, yes, just start knitting with the longer one on your next row. If you're using interchangeables and don't have an extra tip in the correct size you can use a smaller tip for the left hand needle that's already holding the stitches and just knit from it. You can then put the right size tip on the longer cable to continue. HTH
You can't knit the left sock first. Ever.