It's hard to translate without proper context, but given what you provided...
The first image, with Character A's line, does not have an affirmative tone as you suggested. Instead of accusing Character B of not having skills, it is rather a question that ends with the とか listing particle (並立助詞).
The question is:
It could be translated to:
"Do you have any special abilities?"
Character B replies with "どうでしょうか、職業柄器用なほうだと思っていますが". The usage of the volitional form here (verb stem + よう or おう) implies a level of uncertainty and an inquiry directed at the listener.
It could be understood as:
"What do you think?"
"How about that?"
"What's your opinion about that?"
That paired with the が conjunction at the end implies a continuation with contrast. This conjunction is often used to soften the tone of a question or request in Japanese. In this context, I would guess that Character B is insecure about his own image and due to the bad impression that the report gives, so he wants to provide a counterpoint to that.
It could also be that he is completely confident in his handiness and dexterity and socially oblivious when it comes to his report.
I would translate it as such:
"What do you say? I consider myself dexterous because of my profession."
It could be seen as a provocative rhetorical question, or it could be a genuine inquiry depending on who is involved in the conversation. As I said, without knowing the full context, the interpretation is ambiguous.