In other words, is the use of a model to retrieve n and k of a thin film from measured psi and delta essential in ellipsometry? or we can solve this two-equation, 2 unknowns numerically?
You have to use a model to fit the unknown parameters. Ideally you should measure the real thickness of your thin films using a surface profiler instrument.
You can not estimate the n and k without using a model. Best way is use proper model to fit your psi and Delta. To calculate n and k, you don't need ellipsometer software, you can write a small code in matlab.