The “fired off towards Alpha Centauri” bit is the closest thing to impossible. It takes an enormous amount of energy to escape the influence of our sun. It is technically possible, as we’ve done it with the Voyager probes, but there’s no commercial option for it right now. Having remains sent into space is somewhat reasonable, but your destination is effectively impossible most likely.

If you’re wealthy enough, it’s probably an option. You can start your own rocket company and maybe eventually be able to do it, but even most successful rocket companies don’t have the ability to do this yet. SpaceX could, but I have no idea how much mass they could do it with, so it might cost an entire rocket for just this.