WinRAR and WinZip have been on the market for over 25 years - suggesting they contain backdoors is the same as believing in crazy conspiracy theories. No one can stop you, as to whether it makes any sense? Unlikely, except it'll make your life miserable.
If you're scared of running them, you have options including SandBoxie+ or installing them in a virtual machine.
Since WinRAR and WinZip are Windows applications and Windows in itself is closed source, are you OK running it? Literally gigabytes of code.
As for weaknesses? Lots of closed source applications are fuzzy-tested by lots of people. Both applications have tens of millions of installations, so they are quite enticing as an attack vector.
They are closed source, true, does that automatically mean that e.g. Open Source Windows archivers fair better? Doesn't seem to be the case.
The fact that something is open source guarantees neither security, nor the absence of backdoors. It only makes hiding them more difficult. The Linux kernel, the most famous and one of the most important open source software packages, gets fixes for tens of security vulnerabilities monthly most of which are corrected silently.