Is it rude to politely decline a handshake if you are eating?

A lady from another dept came by my boss's office and on their way out, they stopped by my cubicle. I was clearly eating my lunch (a sandwich and fries) and watching Netflix on my iPad. After n boss as making casual conversation with me me, the other lady introduced herself to me and stuck her hand out. I playfully laughed and said "oh you don't want to shake my hand right now, it's dirty, full of grease." I kinda mumbled towards the end. I hope I didn't make a bad impression. She just kinda chuckled and said "oh okay. Well nice to meet you!" I tried to speak to her extra friendly after that to make up for not shaking her hand… Is it always rude to deny a handshake… I'm kind of wondering why she would try to shake my hand if I'm eating anyways.isn't that kind of unsanitary? Haha

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