First, you're not skinny fat, you're where I was over 10 years ago. I am now fluctuating between 85-95 lbs heavier than that (I started lighter than you).
Secondly plateau's are life. Read Dave Tate's "the Dead zone" article. It took me like 2 years to bench 225 and then something like 3 more to get to 300. It's slow work for long limbed guys. I'm over 400 now, but that's after a decade--2+ years to get to 100 kg, 3+ MORE years to get to 140 kg, another 5 years to get to 180 kg. I didn't do everything right, but that's about what it takes for long limbed guys. The ONLY people who ever get past the plateau are those too stubborn to give up. NOBODY else gets past it. That's why you have people without surgeries who have "trained regularly for 15 years" that look like they have never touched a weight.
Thirdly psychologically it might be afraid to risk injury, that is very real and one of my clients suffers from it (also post surgery), but he has almost gotten over it after a year and change of working his limits.
Physically NO it is not your arms. It is your legs and back in squats, back in chin-ups, and probably shoulders and just time spent under the bar. Arms are only usually a problem in shoulder press and bench, and even then it is often something else. Anything else is never arms. Arms should not be doing most of the work with chin-ups.
Fourthly it is probably your program or food intake.
Fifthly You need to add in single leg work for your weak leg. If it is that obviously smaller then it is holding you back strength wise. You need to make it stronger relative to your bigger leg.
Sixth--when you say you can squat 70 kg I assume that is for 5x5? If that is the case, simply increase the weight and keep it at that weight until you CAN squat it for 5x5. It may take a couple weeks or a month or more. If you can do 75 kg for 3x5, then do it and either a) drop the weight on the 4th set by 10 kg, or b) keep the weight the same and try to add a single rep every week.
EXAMPLE: Week 1--3x5, 3, 2 Week 2--3x5, 3, 3 Week 3--3x5, 4, 3, Week 4--4x5, 3, etc. etc.
Recommend Westside for Skinny Bastards version 1. You can find it on here or at Joe Defranco's website. More single leg work involved in that program and it is very good for both size and strength provided you are eating.