Funny you should ask this question, to shake or not to shake? I actually do a regular piece on my blog, "Alyssa's tips on how to impress a woman", and Tip #11 actually touched on this handshake business, from a woman's point of view. This is what I said...
How to Impress a Woman...Tip #11
Confidence is your key! Women are attracted to confident men!! So always present yourself with an air of confidence! This is not to be confused of course with cockiness, no one likes a self-absorbed wanker. But we do like men who are in control.
Your posture and presence is important - walk with your head held high! Look people in the eyes, and have a firm handshake, even with women. The double handshake* is particularly effective with the ladies, so dont be afraid to use it! Speak slowly and clearly, and dont mumble!
Be confident, but not arrogant. Confidence doesnt mean you are superior, it just means you are comfortable and in control. And as I said, we love men who are in control!
*A double handshake starts off like an ordinary handshake, only once your hands are interlocked, you take your left hand and cover her hand, so that effectively her hand is in between both your hands. Try it out with someone, and get someone to try it out on you. Do a normal handshake first, then try the double handshake and feel the difference. It changes a handshake into a more intimate gesture. And dont forget to maintain eye contact while doing this. You may feel a little forward doing this at first if you are not used to it, but have the confidence to use it, it can be very effective.
(Personally, I find the double-handshake very appealing, I don't much liked to be kissed on the cheek unless I know you very very well).