Swimming workout on "original" Apple Watch watchOS 3 introduced a new workout type, swimming. However, this seems to be available only on the new series 2 Apple Watch. 

Is there a way to start a swimming workout on the old Apple Watch (not Series 1, the original from 2015)
No.

Also the original Apple Watch is not made for swimming - it probably won't survive it if you take it swimming every week. The water will simply get in and destroy it.

I would advise buying the new watch for this purpose.