I would not do this under any circumstance. Uber/lyft try to make sure all their drivers have insurance that covers driving for compensation, but a good friend of mine was in an uber-at-fault accident where their insurance denied their claim because they didn't have commercial insurance. Luckily they were on their own time and their insurance covered my injuries and damage and sued the other driver to get their money back.

An accident at work would almost certainly be punted to an OJI claim, and at this company I have no doubt SWA would deny such a claim by saying that you elected to drive with somebody who wasn't properly qualified when they provided a paid-for commercially vetted option. Even if you got cab authorized on your board, if you cab it, I would definitely only CAB it.

If they send you a lyft-link, as they have for me before, then take the lyft/uber, because then the onus is on them to vet. But otherwise, licensed cabby or hotel transportation only.