I always used
Custompac Polystyrene Mug Mailers -
https://www.custompac.co.uk/polystyrene ... search=mug
They do 2 sizes -
- Small (for 10oz Mugs)
- Large (for 11oz Mugs)
I mainly used the Large and there was ample room to wrap the mug in a layer of bubble wrap, for added protection, before placing in the mailer. I never did the quantity of mugs you do but I only ever had one breakage reported.
Incidentally, I used the same mailers for 12oz two-tone mugs with spoons and managed to fit both the bubble-wrapped mug and bubble-wrapped spoon in the mailer.
Cardboard outers are also available if you need them.