“The shul would provide a nearby trashbin if they felt it was a problem to temporarily place it on the table.”
You can’t make that assumption, especially when there is an issur g’zeila involved and it takes about 5 seconds to ask r’shus, unless of course you’re afraid of the answer. Bottom line, however, it’s disgusting and insensitive to the normal people around you and the shulchan aruch states that one is not permitted to davin in front of an object that is mius.