Go ahead and do it. Excavate, lay pipe by hand. Anti-seep collars are a good idea, but handpacking tight clay soils around the pipe is essential. Compact, compact, compact. Leave no gaps in your soil. If you do it correctly, you will give your pond an advantage by managing excess water flow properly.
If it's any comfort, you probably aren't losing many fish through your current overflow. Fish like to find a home, and stay there. Only young of the year, tiny fish, tend to leave, because they usually stay shallow...to keep from being eaten.

Teach a man to grow fish...
He can teach to catch fish...