I think the key check here is not balance, climb or strength but rope use. If done properly, the risk is near zero using a safety harness.
DC 10 to secure the rope at both ends, DC 15 for the harness (special knot).
An improperly tied harness will either:
Fail catastrophically (fall to your doom) or
Injure you (tied improperly through your crotch, for example).
The worst part is that you generally won't know that you've done the harness wrong until someone loses a grip on the rope.
I'd use the following rules:
Fail the Use Rope check on the rope knot and you'll know it and can try again. Fail by more than 5 and you lose the end of the rope you were working on and need to go back across and start over.
Fail the Use Rope check by less than 5 and you can retry. Fail by 5 - 9 and you tied harness that may injure the person if they fall (1d2 damage) Fail by 10 or more and the safety harness offers zero protection against a fall.
I'd allow a Strength Check or Climb Check at DC 15 to cross without slipping.
When looking to set DCs look both to the skill description and the following table:
Code:
Table: Difficulty Class Examples
Difficulty (DC) Example (Skill Used)
Very easy (0) Notice something large in plain sight (Spot)
Easy (5) Climb a knotted rope (Climb)
Average (10) Hear an approaching guard (Listen)
Tough (15) Rig a wagon wheel to fall off (Disable Device)
Challenging (20) Swim in stormy water (Swim)
Formidable (25) Open an average lock (Open Lock)
Heroic (30) Leap across a 30-foot chasm (Jump)
Nearly impossible (40) Track a squad of orcs across hard ground after 24 hours of Rainfall (Survival)