The Pepperidge Farms buns are not safe for sesame. . We use their bread too.
I'll have to check out the King's Hawaiian. I know there is one store here that carries them.
AH but I must comment here! The hot dog buns are safe! They do not carry a sesame warning like the hamburger and when I called - years ago I was told they were safe. Due to their size and shape they are not made with any sesame buns like the hamburger buns are.
When I'm too lazy to make hamburger buns, DD doesn't mind if I split her burger and put halves side by side in a hotdog bun.
I've never found a safe hamburger bun. I make my own thanks to some encouragement from Cookingmom so long ago. I use my bread machine to prep the dough, take it out, shape and let do final rise and bake. If you want them soft, brush hot bun top with melted margarine and let cool. If you like it a with a little crunch, just cool.
I freeze a bunch and thaw as needed. Send these to school for the school cafeteria too. They keep them in the freezer for when DD is going to buy something that needs a bun.
Oh and PF sliders as of yesterday still have a sesame warning. I always look at those but yesterday, along with the warning is a row of sliders with sesame seeds. Poo!