Thanks for this wonderful site and all the Torah it offers. I will be making a simchas in a simcha hall Friday night where all guests will light candles. At the end of the seudah once the candles have burnt out may I ask the AY waiter to move the burnt out candles to the garbage? Is this Amira L’Akum? I should mention that the need for the space the next morning is the issue otherwise I would be ok with it remaining there the whole shabbos.
Regarding telling a gentile to move muktza, in your specific situation you may tell the gentile to move them, although a person should generally not tell a gentile to move muktza without speaking to a rov beforehand.
Best Wishes and Mazal Tov
M:B 276-29, 31.