It would still be a worry if something caught the length of the rope between you and whatever it was tied to, and pulled it down. But in that case, the rope could still be cut.

[He reminds himself that, as much concern as he may have for his remaining family, he'd still left Sansa to rule the North. But he'd left her with a bodyguard devoted enough to her that she'd helped Sansa escape from the clutches of an important lord, consequences be damned... on the other hand, there are people looking out for her here, too.

She probably won't drown.]

Are your arms strong? The training you've been given with the sword should strengthen them.