Well, Sawk is already placed in a lower tier than Toxicroak (NUBL vs RU).
Toxicroak has access to Dry Skin which helps it check some of the strong water threats in the tier like Araquanid, Mega Blastoise, and especially Milotic. The Poison type also helps check the slow bulky fairy types in the tier. It may have lower defenses than Sawk, but it has access to even more recovery other than Dry Skin in the form of Drain Punch. Sturdy on Sawk would be useful, but since entry hazards exist, you have to put a lot of effort of spinning or defogging away hazards until Sawk can safely switch in, but then its pure fighting type doesn't help check the things it's weak to (like bulky fairies, psychic types, etc.). It might 2HKO at best, but it will be KO'd easily by a super effective move. Toxicroak just has a better offensive and defensive typing against the tier.
Overall, I would pick Toxicroak over Sawk.
Hope this helped!
