The Scripture tells us not to take the Mark; therefore there must be some way out of it, probably beheading.
That's not exactly correct... what Scripture tells us to do is 'repent and be saved' so that one never ever ever needs to encounter this situation. To think otherwise is to be planning to go into the tribulation... that is NOT what Christians are told to do anywhere in Scripture. And the way to be planning to go into the Tribulation Period is simply to not become a born again blood bought follower of Jesus Christ. In fact, why can't it be concluded that if a person is planning to go into the Tribulation, they aren't really saved?
"Some way out of it, probably beheading?" I suppose that possibility has some application but this assumes that the people being beheaded know what the Scriptures say and that they have learned all this and have become 'Tribulation Period Christians' before being told that 'you must have the Mark'. That concept of timing seems rather suspect....especially for those multitudes who have never read a Bible, never heard of Jesus Christ etc.
By the way, there is a reason why some of the details concerning the Tribulation Period are unclear... there is simply no reason for God to give all the details for an absolutely horrid period of time that he doesn't want anyone to go through.