How to deal with Westies prey drive? Behaviour

Hey everybody! First post ever!
I really hope you can help me out on this one. So, a family member who is visiting me brought a few days ago a Westie puppy as a gift to me. He is adopted from a rescue. I was happy bc I has waiting for the right chance to go look for a dog but this just made it easier and I'm happy and I love him already! Yesterday when I went to get some supplies to a local pet shop and I decided to go ahead and get some stuff I wanted to buy for my hamsters. At the cash register I told my whole spontaneous puppy surprise to the guy who worked. He looked concerned after he noticed my hamster supplies. It turns out Westies have a prey drive (which is something that I would have found out if I had researched but I wasn't the one who got the puppy:/ ).
Thankfully my hamsters are in my office in a high shelf unreachable to the puppy and I've blocked off the entire hallway so that he won't even reach that part of the apartment just in case (he's got a lot of space still). Even so, I wash my hands thoroughly every time I have contact with anything related to the hamsters because I don't want any "predatory switch" (i dunno) to turn on.
Can someone shed some light on this behavior? If I keep the animals in these conditions will they be able to coexist apart from each other? Or is it better if I return the puppy (if it's even possible) and look for one who is easier to live with small pets?
Thanks everyone for the help!!

I know this is two years late but i thought I’d respond just in case anyone else has the same question. Since Westies were bred to hunt rats and other vermin, they will never able to be fully trusted around any type of small animal like a bunny, squirrel, hamster, guinea pig etc. That means if you own both, the name of the game will be separation, and ideally keeping several layers of it (I.e. the dog is not allowed in the room with the small pet, and it’s in a cage, and it’s up on a high shelf so they can’t get near it if/when they do manage to sneak in)

My male westie just naturally started looking for squirrels in the backyard on his own. Now, as soon as I open the door to let him out, the first thing he does is run to the bird feeder to see if there are any he can chase. The westies I had growing up were the same. They also would love to go after every cat they meet if possible. Training is great and can help them get better at not bolting every time they see something small and furry. Even still, it’s inevitable that nature will overcome nurture at some point and unfortunately these can be traumatic experiences, especially if there are small children around.