The first sentence could describe, for example, a nurse who takes one of his arms in each hand in order to examine them or to hold them in front of herself. In an extreme possibility, the man's arms have been amputated and the young woman for some reason picks them up and does something with them.
The second sentence sounds more dramatic. Perhaps the young woman has slipped over the edge of a cliff and the only reason she is not falling is that she is hanging on to his arms.
Neither sentence is very natural, to be honest and I can't think of an everyday situation where I would use either.
If a woman and a man are walking along side by side and she slips her hand between his arm and his body in order to walk along linked together, we say "She took his arm".