Photo: Haley Nixon from remount technique video (notice she holds her paddle with the hand that she places on the front near side - this is an alternative to the more common paddle in back hand technique Oscar Chalupsky teaches)
To be safe you must be able to remount in all conditions. If you are new to surfsking start practicing in flat water close to shore. When you've mastered remounting on both sides of your ski, start slowly progressing to rougher waters (but avoiding wind blowing you away from shore until you are quite competent). A solid remount will increase your safety AND reduce your fear in big conditions enabling you to paddle with more confidence and catch more waves. Once you've got a great remount keep practicing by occasionally flipping on purpose.
Remounts and wrist leashes
Notice that in all of the techniques described or demonstrated on this page, the paddle is held with only one hand. If you choose to use a paddle to wrist leash - that may impede your ability to remount from both sides using the same remount technique unless you use a quick release with your wrist leash. That would then allow you to let go of your paddle on your leashed wrist side when necessary, but doesn't that kind of diminish the insurance of a paddle leash? You can turn or flip your ski to accomodate the side you need to be on, but that can be difficult and a fair amount of work in rough water. Or as an alternative you could learn both front hand and back hand paddle holding techniques for remount so you can always hold on with your leashed hand and place that hand front or back depending on which side you are remounting from. Or consider using a PFD to paddle leash as another option. Or experiment with a wrist leash that is long enough to not interfere (coiled?) with either side remounts while not being so long that it introduces other tangling problems (see this remount in video)
Some or even much of this advice is not completely necessary in calmer conditions (such as mounting on the upwind side or paddling before you set your feet), but each of these points becomes more and more critical as conditions get rougher:
Richard Forbes on Miller's Run Forgetting Recommendation #2
So you have a bomb proof remount. Are you ready for all paddling conditions?
We don't know which is better for you. Paddle in “back” hand parallel to ski and holding onto far side of ski is demonstrated and taught by Oscar Chalupsky and is very probably the most commonly used. But some very good, experienced surfskiers use and teach the other technique. Some speculate that the paddle in “front” hand perpendicular to ski approach lends itself to the paddle getting hit by waves in rough conditions. Maybe - we'd like to hear about that from folks who use that remount technique. We do know from experience that the paddle in back hand, parallel to ski, technique is not immune to one blade or the other getting caught by waves then diving, sometimes rotating until you can no longer hold onto the paddle. You may have to test these techniques and determine which works better for you or learn both which may solve the paddle in the wrong hand problem if you use a wrist leash.
Notice in the following videos - in 3 out of 4 the hand closer to the front of the surfski is closer to the inside or holding onto the inside edge (closer to the paddler) of the surfski while the hand closer to the back of the surfski is holding onto the side away from the paddler. The exception is the Maliko video where both hands are on or close to the outside, but the paddler's weight is balanced across the surfski by the paddler having their forearm of the arm holding the paddle actually lain across the front of the cockpit and pressing on the closer side of the surfski. The technique that you choose may work better depending on your strength and body type, but whichever way you do it, you want to have it wired for all conditions you will paddle in.
Multiple remounts shown. He admits he makes mistakes and has subsequently updated his technique - read the description and comments.
Oscar shows remount in rough conditions
Danielle McKenzie shows basic remount from another angle