Well, generally, heart rate monitors without chest straps are going to be less accurate than ones with chest straps. The question is simply this: how important is not having a chest strap for you relative to accuracy? If you do decide on one without a chest strap, most require you to to touch the HRM for a reading, but you are not given a continual reading. A few - very few according to my research - are both continuous readings and do not need a chest strap. Namely, the ePulse, the ePulse 2, the Scosche myTrek, and the Scosche Rhythm. I saw another one that I haven't researched as much that had very few reviews, and was something like $250.
Both the Scosches read from a device. Of the 4 only, the ePulses read from the wrist, and of those, I'd recommend the ePulse 2 because it is a newer model.
You can read about continual heart rate monitors without chest straps on my website here:
http://www.heartratemonitorwithoutch...play-monitors/.