I have not and would not do video-type verification. Nevertheless, from reading the boards, ...  
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Your last line -- "Should I be worried about it being recorded, which could lead to possible blackmail or entrapment?" -- is certainly an important consideration.  
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And NO DICK PICS since you don't even know who is on the other end. Some teenage prankster will get you a child sex endangerment kind of conviction.  
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On the flip side, you won't even know where the recipient really is, e.g., scammers. "I'm in your city. See me on video? This is my hotel room." except she is nowhere NEAR your city and is in Russia or North Korea or someplace else. "Send me a deposit and I can host you right away!"
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Hold off until you some more replies with better info. Until then, NO VIDEO!

…use this as a quick screening method…presimably they screenshot your face and send it to a friend in case something happens and she needs to go to the police…they do not have the time to run a background check or check references

i have seen two women who used selfies (not video) as the sole verification, but they were both well reviewed on here so i accepted it. (i think one asked me for my TER handle as well)

btw, cops will not bother with that - they will want to get you into the room as fast as possible because they want your phone with the incriminating texts! and reputable providers will not blackmail you because reputation is everything.  

it all goes back to seeing well reviewed providers