IMO, if you're stuck with run-flats, it's much better to use a can of Fix-a-Flat and reinflate than it is to run the tire without pressure to the nearest tire shop. Far less chance of sidewall damage.
I've done this twice in 15 years (Sienna AWDs). Both times the tire shops understood why I put the goop in. I tipped them $20. Everybody seemed happy, and I didn't have to buy a new tire either time.
But I've moved on from run-flats. Two cans of Fix-a-Flat and a VI air compressor (accept no substitutes!) and a AAA card. At the time, it was the only way I could choose the Hakkas. It was worth it!