Double Handed J-Trash Can

I am not keen on the extremely, and perhaps overly, polite and kind Japanese tendency to encourage guests to put guest rubbish (trash) into the outstretched hands of the host, especially when the item I want to throw away is something that I have had in my mouth like a lolly pop stick. I would be most grateful if Japanese service providers would instead pass me a bin (trash can) but that would for them involve the trauma of showing me the contents of their trash can / rubbish bin: or in a sense showing me their dirty laundry. Perhaps I should take my lolly pop stick home like any self respecting Japanese person.