That's a good question! I think in most cases, people are using the ticket at WDW first and have "leftover" days they use at DL. I know the intent is that you'd have to have the no expiration option, otherwise the ticket would expire 14 days after you used it in Dec. I don't know if the method that DL uses to scan a day from the ticket actually "activates" it as far as WDW is concerned. I have my doubts that anyone at DL or WDW could actually tell you for sure, and I sure wouldn't recommend trying it and risk showing up at WDW in June with an expired ticket.
I also doubt that DL can add the no expiration option to the ticket for you - I think that can only be done at WDW. So, I'd recommend buying the 6 day ticket (or maybe go ahead and go for 10 day depending on the price difference) with no expiration.
I've used WDW tickets at DL, but all had the no expiration option and had been used first at WDW.