27" is as obsolete as the Model T or Volkswagen Beetle -- sure, replacement parts can still be found, but the models as a whole are decades out of production.

My recommendation would be to get some nice Schwalbe tubes to go with your tires -- the AV17 is the one you'll want. While some current production tubes have issues with leaks where the valve stem bonds to the rest of the tube, others may have loose valve cores that need to be tightened. Something to check.

As for the thinner tubes, having thinner walls helps with rolling resistance and weight (more than you might expect). Good ones won't be that much more likely to puncture, but cheap ones may have inconsistent thickness.