Just enough space to fit some zip-decompression code? (I have no idea how much space that would actually take tbh)
Considering ZIP normally uses deflate, which is LZ77 + huffman. LZ77 is super simple and can be implemented in ~30 bytes of code. Huffman tables are fairly simple, but I can't easily visualize some assembly instructions to implement them, however arithmetic coding in all cases exceeds huffman's performance, and can be implemented in about 60 bytes of code. Total = 90 bytes to save 2 kilobytes. Seems worth it.
Note that both these decompressors will be awfully slow, but for just 64 kilobytes of input data I don't think that'll be an issue.