Tldr: borderline impossible, and incredibly expensive.
Each cask weighs 100 tonnes. That would be larger than any single object payload launched into space. There are 'super heavy lift vehicles' designed to carry around that or more, but the only successful ones so far have been single-use and cost over a billion dollars for each launch. There's SpaceX's 'Starship' but that's only designed to get payloads into low earth orbit, and Musk has stated that it can currently only realistically take loads of 40-50 tonnes to low earth orbit - oh, and all of this has also cost an absolute fortune for each launch. Multiply that cost by the many thousands of casks and..
You know what, I'm starting to think you should stop making suggestions.