I would just focus on making the lift.
If you're still transitioning to BW pistols without a counterweight and learning the balance, you'll inevitably have some unnecessary tension because you're fighting to keep stable. The better you get at it, the more you can just do the lift.
I witnessed a successful beast challenge a few years ago by a guy named Andy Speer at an Easy Strength seminar given by Dan John and Pavel.
He killed the press and especially the pullup (he did a double just for fun). On the pistol he lost balance and touched his free leg on his first attempt.
Pavel pulled him aside and said something to him and he nailed the second attempt easily. Afterwards, he said Pavel told him to relax and deliberately "anti-psyche" before the second attempt, then just make the lift. Pavel used it to illustrate that different lifts have different levels of optimal arousal (for example deadlift = high arousal; pistol = low).