By "nag screens" they just mean messages asking you to register (buy) the software you're using.
But you can keep your 50. After
Winzip's trial period expires, it will continue to work indefinitely. All you gotta do is click 'Use Evaluation Version' every time the program starts.
If anyone would rather use a program that never mentions paying, well, Timber mentioned one freebie earlier, & another is
Enzip.
Edited to add direct links to the programs.