While water and electricity may help modify his initial run at the coop, working with him on control behaviors will help a great deal in the long run. Luckily for you poodles are almost the ULTIMATE in obedience dogs.
Self-control and owner-cooperative behaviors really help. Habits you teach and things you INSTILL can prevent accidents and issues.
One thing we train to avoid accidents and escapes, as people go out doors, is to sit before the door is opened at all and to only go through when released. For young dogs we often teach it as sitting on a rug near the door. If pup/dog pops up, no going out.
So teaching a good solid sit or down, on the rug is a great first step.
Once that's solid, you add STAYING on the rug and in position.
To GET what it WANTS - to go out - the dog learns to COOPERATE and listen to you. Failure doesn't result in drama or pain but simply NOT GETTING WHAT IT WANTS.
We teach them to be solid indoors, then inside a fence or on leash, and slowly work toward off leash.
If I take a pup who can sit in the kitchen like his butt is glued there and he does it EVERY single time. As soon as I take him outside... he's a dog, he doesn't generalize, to him it's a whole new world and sit doesn't mean sit any more. That's why a fence or a leash and practice are important. Dogs don't transfer behaviors well. Well, some do, but they're rare.
That's why you hear at the vets office... Sit Sit SIT SITTTTTTTTT, gosh he KNOWS how to sit at home!
Change the place and for the DOG all the rules have changed.
Cooperative behaviors well taught give a dog something to DO to get what he wants.
When I'm working with a dog with particularly strong drives - I use them. Poodles can be like that, herders are another class that also have strong drives.
The dog WANTS to SEE the chickens. To be near them.
So the ONLY way to get near the chickens is to pay attention to ME and DO what I'm asking.
We don't go a step nearer the animals until the dog loosens the leash and LOOKS at me. Bingo a step nearer. Now an excited dog, being excited is likely to hit the end of the leash again immediately. My feet are planted. I'm a tree.
But by the time I'm working a dog near it's biggest brain dead distraction, I've taught the dog to look at me on command and to follow other commands (sit or down or here) so in it's FRUSTRATION and "what the heck is wrong with you!" the dog will eventually either pause and look back or sit in utter frustration and LOOK at me (the idiot not moving). BINGO attention. Reward attention take a step or steps. Until the leash goes snap and the dog's mind is lost again...
REPEAT. It's SLOW (kind of) it takes awareness, patience and time. But it also teaches awareness of you, cooperation with YOU, and YOUR leadership much more solidly and much more swiftly. Cooperative training reaches the soul of what a dog is, a PACK member.
Working WITH what the dog wants and being the PERSON who MAKES IT HAPPEN, is powerful dog training juju.
You don't just change it's outward behavior, you change your relationship to it, you become important to what it wants. You become a FOCUS.
Teaching a dog what to DO, to get what it wants is much easier in the long run than trying to make a not-to-do.
If I yell LEAVE IT at a dog racing for the fence and it stops, then it certainly won't be jumping on the car coming up the drive. Chasing stock any further. Jumping up on someone. Leave it, is an active command, a to do - turn away.
Yes, water and shock can provide reinforcement for commands already taught. But applied in a vacuum, without a foundation of What it should DO, it is less fair and can add stressors a rescue, sensitive or young dog may not do well with.
I lay a foundation. Then if I AM ignored, then there's a place for punishment. But it is my responsibility to teach first, the range of behaviors I require that will get the dog what it does want.
Chase drive is not prey drive, the dog wants the chase.
Only a dog that kills is in hunt drive and hunting is not prey drive.
Full prey drive animals EAT what they kill.
Bird dogs properly fall into chase drive, in most cases.
In the case of pet bred dogs, of course there's no control, and been no breeding or selection to avoid dogs that would hunt or eat prey. So, you are wise to be careful.
Good luck. Poodles rock. If you do some real foundation obedience work with a poodle you will LIGHT UP his soul. They're made for it.