Browning no longer chambers the WSM in the SS Stalker line for southpaws (still offer it in traditional chambering - 270, 3006, 7mm mag, 300 wm, etc). I believe they did up until last year though, so you could try asking your shop to try to sourcepre 05 modelor look for a used/trade in. It is available in the wood Abolt as mentioned.

Best of luck