Israeli deputy Minister of Health Yaacov Litchman wouldn't shake the hand of his Belgian counterpart, causing a mini-dipomatic tempest in a teapot.
So what does an observant Jew do when a women extends her hand?
Observe the Torah by all means, but let's do our best to avoid embarrassing others.
I try to keep a few hard candies in my pocket when on tour. If a woman extends a hand, I drop a hard candy in her palm. The potentially embarrassing situation turns into smiles.