Standard Poodles are the unsung hero of hunting dogs. Super hunters and excellent water dogs.
Your situation would depend on size and how the cross worked out.
If he wants to go play with the bird, shoot him. I am not a dog expert, but crosses sometimes work out, sometimes not.
I had one that was 3/4 Black lab and 1/4 Irish. Smart,strong, excellent hunter. Lived 17 years, and was the kids' dog too.
I guess you just have to take a chance. In your case I would want all the size I could get.
HM