Is there any IP problems with the compression algorithms involved?

Why would there be? gzip and zip (yes they are related) were precisely developed to be free of IP encumberment. See Zlib's homepage:

zlib is designed to be a free, general-purpose, legally unencumbered -- that is, not covered by any patents -- lossless data-compression library for use on virtually any computer hardware and operating system.

Zlib is a library that handles both gzip and zip compression, the canonical Perl interface to it is Compress::Zlib, which in turn is what Archive::Zip uses for the actual compression and decompression of the ZIP archive files.