Все требования

public static void main(String[] args) throws IOException {
        HashMap<ZipEntry, byte[]> zipContentMap = new HashMap<>();

        try (ZipInputStream zin = new ZipInputStream(new FileInputStream(args[1]))) {
            ZipEntry entry;
            while ((entry = zin.getNextEntry()) != null) {
                try (ByteArrayOutputStream entryContent = new ByteArrayOutputStream()) {
                    int count;
                    byte[] buff = new byte[256];
                    while ((count = zin.read(buff)) > 0) {
                        entryContent.write(buff, 0, count);
                    }
                    zipContentMap.put(entry, entryContent.toByteArray());
                }
            }
        }
        String entryToAppend = "new/" + args[0].substring(args[0].lastIndexOf("/") + 1);
        try (ZipOutputStream out = new ZipOutputStream(Files.newOutputStream(Paths.get(args[1])))) {
            out.putNextEntry(new ZipEntry(entryToAppend));
            Files.copy(Paths.get(args[0]), out);
            out.closeEntry();
            for (Map.Entry<ZipEntry, byte[]> entry : zipContentMap.entrySet()) {
                if (entry.getKey().toString().equals(entryToAppend)) continue;
                out.putNextEntry(entry.getKey());
                out.write(entry.getValue(), 0, entry.getValue().length);
                out.closeEntry();
            }
        }
    }

public static String buildEntryPath(String filePath) {
        if (filePath.contains("/")) {
            return "new/" + filePath.substring(filePath.lastIndexOf("/") + 1);
        } else return "new\\" + filePath.substring(filePath.lastIndexOf("\\") + 1);
    }

class ZippingFileVisitor extends SimpleFileVisitor<Path> {
    private ZipOutputStream out;
    private Path source;
    private String toAppend;


    public ZippingFileVisitor(ZipOutputStream out, Path source, String toAppend) {
        this.out = out;
        this.source = source;
        if (toAppend.contains("/")) {
            this.toAppend = toAppend.substring(toAppend.lastIndexOf("/") + 1);
        } else {
            this.toAppend = toAppend.substring(toAppend.lastIndexOf("\\") + 1);
        }
    }

    @Override
    public FileVisitResult postVisitDirectory(Path dir, IOException exc) throws IOException {
        Files.delete(dir);
        return super.postVisitDirectory(dir, exc);
    }

    @Override
    public FileVisitResult visitFile(Path file, BasicFileAttributes attrs) throws IOException {
        if (file.getFileName().toString().equals(toAppend)) {
            Files.delete(file);
            return FileVisitResult.CONTINUE;
        }
        ZipEntry entry = new ZipEntry(source.relativize(file).toString());
        out.putNextEntry(entry);
        Files.copy(file, out);
        Files.delete(file);
        return super.visitFile(file, attrs);
    }
}