You are using predominantly machines so the exercises I would recommend would be seated rowing, lat pull downs, and pull ups for the biceps, bench (chest) press, shoulder press and bench dips for triceps.
Being distracted by work I forgot to ask how often you train and what kit you have available. any guidance is good.
Difficulties you will have are serious because the damage is to both sides. Using machines is good in many ways regarding safety, but you could be working out of balance or unevenly without knowing it and the machine would compensate. Good news is you don't drop weights on yourself using a machine, that's useful.
Because your body won't tell you if you are causing damage you will have to be uber vigilant on technique and try to ensure the feedback you get is even both sides. I cannot guarantee there will not be damage to the skin etc. this only stretches 5% as it is scar tissue even less so. I had a bunch of scars removed years ago, club insurance covered it so I thought what the heck.
If there is any discomfort from the skin stop immediately, It will not stretch if you keep re-damaging scar tissue, trust me on that one. There is a strong chance that this will mean doing some of the exercises with limited movement, what those who don't know will likely call cheating, that is something that will change over time, better to do a useful half movement than damaging whole one.
Future warning. You will be building strength in limited movement. When this changes and you can do it all you will be weak in the area you haven't done and this will be annoying. Unfortunately it is a case of deal with it and work through the annoyance, something you will be used to.
I thought I'd take this to a new thread - apologies again for hijacking the other thread.
I use the resistance machines at the gym which covers as you've mentioned lat pull downs, and pull ups for the biceps, bench (chest) press, shoulder press and bench dips for triceps.
I am very careful as although the surgery was 18 months ago - I still feel that I need to be wary of stretching the scar tissue. And your spot on - some of the movement is limited with regards to how far I can push or how much I can pull. It certainly is a weird sensation of not being able to feel your underarm area. I just want to ensure that I keep working the muscles so they don't lose 'texture'?
I really appreciate your advice with all this!