I'm assuming you are much more conscious about this issue than I am (that's fine btw, people have various levels of germophobia) , but practically my whole office block do this without any noticeable health epidemic.
Also standard coffee shops (the Starbucks kinds) always have industrial scale utensil washers that rinse boiling water/UV radiate the utensils. Assuming a government issue the appropriate law, the coffee shops will be able to ensure your container hygiene just fine.