Oil finishes and oil/varnish blends (which is what most "Danish Oil" and similar finishes are, combined with a lot of thinner) work just fine and paddles finished with them don't absorb any appreciable amount of water.

If you epoxy finish a paddle, you should varnish it for UV protection. Personally, I don't like hard film finishes, as they will all eventually crack, allowing water into the wood and trapping it there, ultimately causing rot. I find oils and blends to be much easier to live with, plus I like their look and feel.

BTW, unless you've already have bought the "penetrating oil" finish that you're thinking of using, I would suggest buying varnish and pure tung oil (or "boiled" linseed oil) and mixing your own. With the commercial finishes, you're paying a lot of money for a product that's typically more than 50% mineral spirits. Thinning really doesn't help penetration significantly, it makes the resulting finish more porous and it requires more coats to achieve a satisfactory finish (if it's 50% thinner, it makes sense it would take twice as many coats as with a product with no thinner). Also, if you blend your own, you can play with the oil/varnish ratio to get the combination of look. feel and durability you like. 50:50 is a good starting point that will produce a finish that looks and feels like oil, but is considerably more durable than oil alone.