As both ZIP and CAB are compressed file archive, you could simple repack one to another - preferably with a file archiver that supports both formats at once.
Convert WinZIP Compressed ZIP archive to Windows Cabinet Compressed Archive.
We have found 3 software records in our database eligible for .zip to .cab file format conversion.
Microsoft Windows software - convert zip to cab on Windows
Freeware file compression tool
Convert from zip file format
The tables with software actions are a good pointer for what a certain program does with various file types and often may give users a good hint how to perform certain file conversion, for example the above-mentioned zip to cab. However, it is not perfect and sometimes can show results which are not really usable because of how certain programs work with files and the possible conversion is thus actually not possible at all.
One of the many available file compression utilities
A freeware archive utility that supports many archive formats