Recoverably recompress gzip files into zstd, preserving original checksums?

I need to archive a lot of gzip-compressed data. The problem is that compared to zstd, gzip is wasteful, both in terms of ratio and CPU time required to decompress the data. Because of that, I want to recompress the data into zstd. Unfortunately, I need to be able to reconstruct the SHA/MD5 checksums of the original compressed gzip files, in order to prove its origin. Is it possible? If the gzip algorithm was deterministic, that would be trivial, but I don't have access to information about which version of gzip was used, what was the compression level etc.