Should I submit my SAT scores to Cornell with my transfer application?

The Cornell website says that for transfer students, they do not have to submit their SAT/ACT scores with their applications ‘if’ they have not previously taken them. Although I have taken the SAT test during my high school junior year, I would prefer not to send them to Cornell, as they would probably hurt my chances of admission. The Cornell transfer admissions page also stated that if transfer applicants did previously take a standardized test, then they should submit it. Could I tell them I never took a standardized test, so I don’t have to submit my SAT score? Does Cornell have any way of knowing that I have taken the SAT if I don’t submit it? Do Ivy league schools in general find out that a transfer student has taken the SAT? Thanks.