Did the Apostles Die as Martyrs?

This video, from Stand to Reason, suggests that we have good reason to believe that, though it is an argument from silence. 

My view is that regardless of how they actually died, when you say something like this, from Acts 4: 9-10, 

If we are being called to account today for an act of kindness shown to a man who was lame and are being asked how he was healed,then know this, you and all the people of Israel: It is by the name of Jesus Christ of Nazareth, whom you crucified but whom God raised from the dead, that this man stands before you healed.

you are telling the people who had the power to get someone executed, namely Jesus, that you are sufficiently convinced of what you are saying that you are willing to die for it. This does, it seems to be, support the claim that the Apostles strongly believed in the Resurrection, and would undercut conspiracy theories. A skeptic needs a theory that explains, and does not deny, this sincere belief.