If the vacuum pipes are more or less solid then probably the easiest way would be to get a plastic grocery sack or small wad of cloth. Tie some twine or fishing line to it. Shove it in one end (should be loose but take up most of the cross-section, you do not want it packed in) and go to the other end with a shop vac and suck it through.

Then you can tie the cable to the twine and pull it through. No reason not to keep a length of twine in the pipe for future runs.