I'm sorry, I'm on the suck it up side. I have taken care of business the day I had a baby and finished a job after a fall that broke a vertebrae and dislocated my jaw... then I went to the doctor. If you are in business for yourself and did not think to have a contingency plan in place, you should do the cake.
I was sick one time when a cake was due. My husband is a physician and he said that with a mask and gloves, it was fine. And as posted earlier, the germs don't live but so long. Also, once you have the symptoms, you have actually been contageous for days and are probably at the end stages of contamination. Doctors don't get sick because the wear gloves.
Anyone in business should have a backup plan before they accept their first order. I am getting ready to sign a lease on retail space and the landlord reminded me that not being open was not an option and would be stipulated in the lease. This means snow too. For retail, that would mean a backup employee behind the counter if I look sick.
It may take 10x longer, but on short notice, the person may not be able to get a substitute baker.