public int Action(string typeJob,string fileInput, string fileOut)
{
    if (FileExistCheck(fileInput, fileOut))
    {
        using (FileStream sourceStream = new FileStream(fileInput, FileMode.Open))
        {
            using (FileStream targetStream = File.Create(fileOut))
            {
                switch (typeJob)
                {
                    case "compress":
                        using (GZipStream compressionStream = new GZipStream(targetStream, CompressionMode.Compress))
                        {
                            sourceStream.CopyTo(compressionStream);
                            return 0;
                        }
                    case "decompress":
                        using (GZipStream decompressionStream = new GZipStream(sourceStream, CompressionMode.Decompress))
                        {
                            try
                            {
                                decompressionStream.CopyTo(targetStream);
                                return 0;
                            }
                            catch (InvalidDataException)
                            {
                                Console.WriteLine("Возможно путь к архиву указывает на файл иного типа");
                                File.Delete(fileOut);
                                return 1;
                            }
                        }
                    default:
                        Console.WriteLine("Первый аргумент указан неверно");
                        Console.WriteLine("Следует выбрать compress или decompress");
                        File.Delete(fileOut);
                        return 1;
                }
            }
        }
    }
    else return 1;
}

public async Task<int> ActionAsync(
    string typeJob,
    string fileInput,
    string fileOut,
    CancellationToken token)

sourceStream.CopyTo(compressionStream);

await sourceStream.CopyToAsync(compressionStream, token).ConfigureAwait(false);

var cts = new CancellationTokenSource();
ActionAsync(..., ..., ..., cts.Token);

cts.Cancel();