Is it permissible for a paternal aunt to shake hands with the male grandchildren of her siblings?

The paternal aunt or a sister of the father is considered a mahram to her brothers' children and their grandchildren. It is permissible for the aunt to shake hands with her brothers' grandchildren, provided there is no fear of fitna (temptation/strife). Shaking hands with a mahram is originally permissible, as long as there is no fear of fitna. If fitna is feared, then one must refrain from it.