OK, two options for now:
1: Using your outdated Swiss passport for buying the ticket and showing the conductor, using your valid Argentinian passport for border controls
2: Using your valid Argentinian passport for buying the ticket and border controls, showing the residency paper without date to the conductor to prove your Swiss residency
So, you are definitely fine with border controls, only thing to worry are conductors who check your ticket and passport thouroughly. In my experience, about 1 out of 10 conductors check the passport/id together with the InterRail ticket itself...
I'd say, you could have arguments with a conductor either way...but you should be able to explain your situation - as long as the conductor can understand you.
Have you thought about renewing your Swiss passport? Or is there any kind of other ID existant in Switzerland that you could easily get as a Swiss resident - because you dont neccessarily have to use your passport to get the InterRail ticket.