There are two separate checks for flashable zips -- md5 checksum and zip signature check. The "failed to vertify whole files" message seems to come from failed zip signature check. To fix it, you need to sign the zip with a valid key/certificate.
Custom recoveries shouldn't require signed zips nor md5 checksums, unless you turn the features on in settings. Are you using the stock recovery? If so, whether you can install a privately signed zip depends on the manufacturer. If the stock recovery accepts Google's test key, then you can sign the zip with that certificate. Otherwise, you would need to sign the zips with the manufacturer's key, but I don't think that's public knowledge. I think most people just install a custom recovery instead.