Hi
Whilst the Workout app on Apple Watch does not include paddling / paddly training as a main activity type, your workouts can still be named as Paddling.
Record your workouts by selecting Other as the activity type. Upon ending the workout, tap on the option to Name Workout, where available labels include Paddling.
More information:
When recording a workout via the Workout app, choosing the activity type that most closely matches your workout enables Apple Watch to use the most appropriate sensors and data sources when estimating the results, including using tailored calorie calculations for preset activity types.
For activities that are not included within the list or that are not sufficiently similar - including paddle boarding - record your workout under "Other".
This credits one minute of Exercise for each full minute of the workout. Active calories for Other workouts are estimated at a rate equivalent to a brisk walk or based on data recorded by the heart rate sensor, whichever is higher. Note that neither a route map nor distance are recorded for Other workouts.
More information:
Work out with your Apple Watch - Apple Support
About workout types
If you would like to submit a feature request to Apple in respect of paddle boarding being added as a main activity type, complete with route map and distance tracking, then you can do so here:
Feedback - Apple Watch - Apple