The standard restaurant POS systems for table-service restaurants in the US still use swipe-and-sign, so as long as your card has a mag stripe you'll sign the slip like everyone else--even if your card's EMV implementation doesn't support signature at all.

PINs wouldn't work with the current setup because the charge is finalized later based on the handwritten tip amount on the receipt.

As for the OP's question about embarrassment, as an American living in Europe, I use my CSR 99% of the time because I want those sweet, sweet airline miles (well, that and I get paid in USD so the zero FTF plastic is cheaper than paying from my EUR account). My local cards are reserved for times that the US card won't work.