The iOS/MacOS Compression Framework would be the fastest and cause no additional bloat
re: https://developer.apple.com/documentation/compression?language=objc
While it does not support creating a "Zip"-based internally formatted file, it does support multiple compression algorithms.
Apple recommends using COMPRESSION_ZLIB:
The zlib compression algorithm, recommended for cross-platform compression.
There are a multitude of (de)compression tools on that can decompress zlib raw based files, but to make it "easier", you can include a header so gzip (Windows, macOS, and Linux) can handle them without further changes. (You can also add a CRC-based footer to the file, but it is not really needed, unless you are comparing the mobile and server CRCs of your zip files already...)
Raw zlib w/header Example:
using (var fileOriginal = new FileStream(inputFile, FileMode.Open))
using (var fileCompressed = new FileStream(outputZip, FileMode.Create))
using (var compressionStream = new Compression.CompressionStream(fileCompressed, System.IO.Compression.CompressionMode.Compress, CompressionAlgorithm.Zlib, true))
{
var header = new byte[] { 31, 139, 8, 0, 0, 0, 0, 0, 0, 0 }; // \x1f\x8b\x08\x00\x00\x00\x00\x00\x00\x00
fileCompressed.Write(header, 0, header.Length);
fileOriginal.CopyTo(compressionStream);
}