If you are applying with legitimate companies, this is a secure process. It is in the companies' best interest to provide a secure process. Doing so may lessen liability. The companies want your social security number so that they can pay you and, if necessary, issue an I-9 for your income if that meets the $600 threshold. One alternative is to obtain an EIN. EIN = Employer Identification Number. Some companies accept this number instead of a social security number, and some shoppers use it for their businesses (even if they are mystery shoppers who work alone and do not have employees). Some people think that the EIN is less personal than a social security number and believe that it might be harder to hack than a social security number. You can decide what is best for you.
Nature does not hurry, yet everything is accomplished. - Lao-Tzu