Ask your speech audience to write their questions down on note cards

The Toastmasters International guide for trainers, TRAINING BASICS Getting it right, Making it Work, discusses dealing with difficult participants including The Silent Type, The Talker, and The Interrupter.

 At the Faculty Focus website there was an excellent article by Professor Meriah L. Crawford on October 13, 2017 titled A Simple Trick for Getting Students to Ask Questions in Class. She described getting a magic increase in feedback from passing out note cards and asking students to just write down their questions. If there are multiple questions, you can shuffle the cards to keep the responders anonymous. When there are multiple questions on the same topic, you can combine them. Written questions can draw out The Silent Type.     

This strategy also will work for speeches. Getting the questions in writing will help them be more organized, and shut down The Interrupter (a long-winded audience member who just wants to hear themselves talk). 

Professor Crawford also suggested that for large audiences you could ask for questions online (perhaps at Twitter).

The image of note cards came from openclipart.