Some thoughts on the topic...
(FYI... I'm not a doc... but volunteer EMT for 18 years.)
* Artificial respirations in a pulseless individual are pointless. Without circulation, no tissue, (including brain), oxygenation will occur.
* If the issue is not being sure of pulse, I'd suggest trying to be more sure of this by...
+ practicing finding and testing for pulse in BOTH carotid, (neck), arteries. (Yes, some people may have weaker pulses and bobbing in waves can make this difficult.) And give yourself a bit mroe time to relax and try to find it. You're going to throw a couple of rescue breaths in first anyway. It's more important to know what you're dealing with and do the right thing rather than do the wrong thing quickly.
* The "pericardial thump" or "precordial thump" is kind of an unknown. While there's no way I can see you can really do effective CPR without a firm surface behind the victim, MAYBE you could try that sharp blow to sternum, BUT, there is nothing I've ever read anywhere that indicates this as an accepted protocol for diving emergencies. (And I'm not quite sure how you'd effectively do it in the water with BC's and wetsuits anyway.) The thump is administered with one sharp closed fisted hit to the mid/lower part of sternum. The theory is that it can convert some heart rhythms back to sinus rhythm. In the end, it's your call and if the person's dead, it can't hurt. If they do have a pulse, and you do this it could; however hurt. If someone SEES you do this, you could also have a legal issue unless you have some really good reason why you did it. (You'll need to check the Good Samaritan laws in your state for details... but usually, these are based on what a "prudent reasonable person would do." Morever, if you do have a CPR card or training, and you go beyond that "standard of care" you may not be just a "reasonable prudent person" but a trained person who did something not indicated by their training.
For details on the thump, see... Colqhhoun, M et al. 1995. ABC of Resuscitation. 3rd edn. BMJ Publishing Group. London (or just search for "precodial thump" in Google or something.)
Remember, the way CPR actually works is part using pressure to push blood, but also may stimulate the electrical parts of the heart to beat and push blood. There was a REASON for the arrest. If it was trauma or something reversible, great. If not, it's a done deal.
The bottom line though, is CPR alone, even if almost immediate, still has a tiny percentage of bringing someone out of it. (Like under 5%.) What you really need is an Automated External Defribrilator, which supposedly increases chances to a whoppingly different 43/% IF CPR was started immediately and defib happens within 8 minutes... chances decreases 10% every minute thereafter that there's no defib. Without defib, sorry... but chances are real slim.
Details:
http://www.delmarhealthcare.com/pdf/ch25.pdf
Lastly, and most importantly, protect yourself. If you are bobbing around in the seas, you have to be concerned with your own survival as well as the patients. If you are not fully buoyant and become exausted assisted a victim, you could have problems of your own. You've now doubled the workload of anyone else coming to assist as well as put yourself at risk. If you ever have the unfortunate luck to have to do this; do what you can, but don't kick yourself if things don't work out like on television. It's rarely like that.
Scott