I put the cord in first and then the hose.
The hose is harder to fit than the cord, and I only unwind as much cord I need to get to the outlet after I take out the hose.
I do not think I would be comfortable suggesting shortening it with the warranty implications, and I have a lot of tools that have short cords on them to get local power into the machine. The only tools I have not considered modifying are the Festools.
In theory: it should be easy. Just get a cord from the shop and totally replace the existing one, but that assumes you have the electrical skills to not get shocked, and if others are using it, then there is liability to consider.
In practice: I would suggest you send it to Festool to do that for you, as that is the safest from both a safety and warranty perspective.