You're worng. How's that? JK
Once any inspection goes out of date, the ENTIRE aircraft becomes unairworty in the eyes of the FAA.
Again go to faa.gov, download a ferry permit, fill it out, fax it to the FSDO, they will aprove it, make the flight under the conditions of the permit. It's quite painless. In this case it's doubtfull you will even need an A&P to sign it.
As opposed to taking off, and getting ramp checked when you land at the other airport. Or even just worrying about that happening.
If the transponder itself was only broken, you would be fine with just calling the TRACON. But this is not the case, it is perfectly fine, only out of date therefore causieng the whole aircraft to become unairworty.
Stupid logic, I know, but that's the FAA. They care about paperwork, not safety.
You know what? For some reason the transponder won't turn on and the light won't work (jk) so its inoperative. Boooya Calling the ATC facility and getting a waiver. The airport is 7 miles away.