Fairly simple suggestion here. The two other chain weapons both stand out in that some of their standard attacks incorporate a saw rip effect to them, even without activating it - the Chain Axe’s light attacks have a saw rip effect, while the Eviscerator’s heavy attacks have a saw rip. In the latter case, it uses the “Heavy Attack Sawing Damage” value listed under Shredder, while the former has a dedicated stat line for light attack rips.
Meanwhile, none of the attacks on the 1h Chainsword incorporate a rip effect without first being activated. However, you could squeeze it in on one spot - the push attack follow-up stab. This particular attack is already fairly lackluster in damage, and not very useful when fighting hordes, so feel it wouldn’t be disadvantaged by adding a stick and rip effect to it.
Plus, the attack is already an homage to Dan Abnett’s Ibram Gaunt, who wins a chainsword duel against his Uncle Dercius with a surprise stab, complete with rev.