If damaged pedal does not interfere with cable glide - the techniques used for a broken cable mentioned above can work for an unusable pedal on one side.
Paddle clamp breaks, blade is damaged or falls off - You may prepare yourself for breaking your paddle by practicing paddling with half your paddle. Store half your paddle on your aft deck and paddle with the other half. Practice in progressively rougher water.
Broken Paddle 2018 (also evidence for Prone Paddling technique with the ski right side up, although then you may have to deal with keeping the rudder straight if you do not have a self correcting rudder)
You have lost or broken your paddle, cannot effectively paddle for some reason, or cannot stay upright in your surfski.
If conditions are not too rough, you may be able to lie on top of your surfski and hand paddle.
Turning your surfski upside down and lying prone, straddling the bottom side up with your weight low and head down can be more stable on some skis than lying prone on an upright surfski, providing you the ability to make adequate progress back to shore.
Which way to turn your ski and lie on is better for you and your ski? Is this technique at all practical for you and your surfski? You will have no way of knowing unless you have tried it, preferably with controlled, safe tests (close to shore, on shore wind, clothed for the weather and water, help readily available if needed, etc.) in rough enough conditions.
Even if you can make little progress paddling using this method, lying on top of your surfski will allow you to stay warmer than swimming will. That may make a critical difference by allowing you to stave off hypothermia until rescuers find you.
Practice can help you determine what techniques are most effective under various conditions. You may have to abandon your paddle also in order to swim more effectively if there is little or no prospect for recovering your boat.
Stroke with paddle - If you are very bouyant (such as when you are wearing a dry suit) You can float on your back and back stroke with your paddle on both sides
One arm stroke holding paddle with other hand - hold your paddle just below the blade and point it in front of you and swim with your other hand. But in this situation keeping your paddle should be low on your priority list. Use whatever swimming style works best (test them!).
Two arm swim stroke with paddle? Video demo (although note the swimmer also has fins on)