Train with the paddles, start small and grow, a good paddle to start with is the Speedo Tech (small version). The cadence of your stroke will decrease but the power of your stroke will increase (hopefully!) a bit like going up a gear when riding a bike. Once your shoulders are used to the paddle do some timed 400m sets with and without paddles to make sure you are actually going faster with the paddles! If not then either change the way you use them or don't bother with them at all!
For my first two OtillO Uto races I didn't use hand paddles, then I tried with the small version of the Speedo Tech paddle for OtillO Engadin. They grip the water well and being small didn't put too much extra strain on my shoulders. I have now worked my way up to my current favourites the TYR Catalyst 2 paddle.
I have found I can go up to around 10% faster over 400m. I also believe it has improved my stroke technique. Be mindful of the shape of the paddle and it's movement through the water, you don't want to waste strokes with slicing and "wobbling" the paddles through the water. Using hand paddles is a great opportunity to slow your stroke down.
Of course always remember the principle of streamlining for efficient swimming.
It's now 3 years since I first tried paddles and only now do I feel completely comfortable with them so give them time and start small. It is unlikely that you will instantly love them... try a little patience.
Many swimruns take part in exposed sections of sea and lakes so do some training with the paddles in windy conditions and swell, get used to handling them in waves and rough water. You may want to use smaller paddles if conditions are particularly rough - test, test, test.
Recently Seal blades asked me to test their product. Originally designed for surfers, they may be worth giving a try for swimrun. They feel better than expected in the water and they didn't put any unexpected strains on my shoulders in testing.
I'll be doing a few more tests with the Sealblades, but I'll be sticking to my TYR paddles for racing.