Ladders
Should only need one hand.

You need both hands free to climb a ladder. I suggest it should be reduced to one, as you only really need one to do it IRL. This would make losing an arm/hand less onerous and would still prevent you from doing silly things like hauling furniture up ladders.

I'd say you should be able to attempt the climb without use of both hands, but it should require some serious agility to pull it off over multiple stories. I can certainly climb a roof ladder one handed. I never would, but I could pull it off. Ladder of a water tower? No way I would even attempt it one handed.

Real world, It depends on the ladder. I was always taught to always try and maintain three points of contact when climbing a ladder to ensure safety (so only move one hand or foot at a time) . Most any ladder with rails (the vertical outside bit that holds the horizontal rungs between them) can easily be climbed with one hand as the one hand can pretty much slide along the a rail the whole time. The ones without rails can still be climbed with one hand but involve frequently only maintaining two points of contact. Someone with reasonable agility and some experience can still manage just fine.

My opinion after all of that ranting: Either just allow one handed ladder climbing or allow it with a stat/skill check.

A ladder is just an exit in a room. Sometimes really big ladders are rooms themselves but afaik coding ladder-room-specific combat is not something anyone has had time to do.

I just want one armed people to be able to get around the Mix.

This is supposed to be a hindrance. Get a cybernetic arm. Those are literally coded for a reason, instead of skirting around obstacles and proposing changes to make your life easier and cybernetics pointless, utilise the cybernetics available to make your life easier. It's CP.

Cyberarms are not a realistic solution for anyone but maybe a corporate character who lost their arm in that one accident that one time. It's just not cost effective.