I think that shaking doesn´t contribute much to catching the flu. It´s more important to maintain a proper room climate (enough humidity and not too warm) to keep the muscous membranes intact. Ventilating the room frequently also helps to keep the flu at bay (took some work but it´s done in the office too). Frequent walks in the fresh winter air help a lot too.
I would avoid to shake hand with a person with an acute infection. That´s not because of the skin contact but because it allows to keep some distance.
I haven´t caught the flu or a cold for more than a decade even when my colleagues had to take sick leaves after coming to the office until the infection forced them to stay in bed.