How many nights do you have for this trip, only 1?
You'd probably be better off visiting Yosemite, stay the night and return to SF or Sacramento then fly to Las Vegas.
Check for chain requirements at http://www.dot.ca.gov/ for road conditions and chain requirements, not at the car rental agency.
You have 2 routes from Yosemite to Las Vegas, both would be best with an overnight somewhere.
The very boring ugly route of Yosemite-Bakersfield-Las Vegas is a solid 8 hours at least and a complete waste of time, unless you make a detour to death Valley it's a horrible tedious route, fly!
The other route is via South Lake Tahoe, incredibly scenic but you'll need chains to be safe and an overnight somewhere.
Chains-cables are only about $50-60 bucks and easy to put on, lot of places have chain-cable people to put them on for you on the side of the road, they know where the chain-cable requirements are.
You'll probably need chain/cables in Yosemite as well in February, most likely.