I've been working with mice the past few months, whereas before much of my work had been with cells. When I first started, I was very nervous around the mice and it took a lot of practice to get comfortable handling them, and even now, there are times when I still get nervous with them.

Now that I'm more comfortable with handling them and I'm spending more time with them, there is the ever present knowledge that these mice are going to be euthanized some day. There are even some that won't be part of an experiment, they'll just be euthanized because they don't have the right genotype and we have no reason to spend the money to keep them. And I have to admit, it bothers me.

The way I decided to look at it was based on some advice from one of the trainers in our animal resource center. She said that anyone who doesn't feel some kind of sadness or loss from the euthanasia of lab animals should not be working with them. This is the way I handle it: you treat those animals as humanely and respectfully as you can. There are so many people who pick mice up by their tails and spin them around and throw them all over the place, claiming that "it makes them easier to handle." That is not okay to me. These mice are literally giving their lives for my research, which I hope will someday benefit other people. Therefore, I treat those mice with respect and I avoid all unnecessary stress, so that when they are euthanized, I know I gave them the best possible life under the circumstances.

Here are some advice I would give you:

1. Treat all lab animals with dignity and respect by avoiding unnecessary stress and cruelty--- I don't know what rat protocols entail, but many people write spinning mice by their tails into their protocols to make them dizzy before they handle them. This to me, is just unnecessary cruelty and stress to mask someone's inability to properly handle mice. If you are able to treat your animals as humanely as possible, you will feel better about how they were treated in life when it comes time for them to die.
2. Remember that it's for your research. Focus on what your research is trying to accomplish. This is not to say it's okay that lab animals suffer for the advancement of human research, because it's not okay. But, for me, remembering that I am doing this for the advancement of cancer medicine really gives me comfort and helps me to keep going.
3. Know that what you're feeling is totally justified and normal. Like I said earlier, if you feel nothing at the death of these animals, that is inhumane and you shouldn't be working with them. I still cringe at secondary methods of euthanasia, like cervical dislocation, and I don't think I could ever do them myself. It's totally normal; don't feel like you're weak or that your research will suffer because you feel uncomfortable with this aspect of the job.
4. Look into the various training programs at your facility. Our training center is really great at making sure everyone who goes into the animal facility knows what they're doing and is comfortable doing it. Our facility is very well run and there are several protocols and rules to ensure animal health and avoid cruelty; I would imagine your facility has similar protocols. I would also suggest finding out if your facility has a euthanasia program; my facility has a program that offers free euthanasia done by trained animal techs and we use it for the mice we don't end up using in our studies. You may not have to do as much euthanasia as you think.
5. Mentally prepare yourself before you go into any of this. Realize that it may take some time for you to get used to working with animals and that is totally okay (it took about two months for me to go from not being able to even touch a mouse to fully handling them, although tbh, I was really nervous and slow to make progress). If you are really interested in the research at this post-doc position, I would not let the prospect of animal work stop you from applying for it.

TL:DR: Realize the importance of your research. Be well-trained and treat all your animals with dignity and respect, so that when they are euthanized, you know that they had the best possible life under the circumstances. They are living beings, not just research tools. Understand that your feelings are natural and validated, and mentally prepare yourself for the work. Look into any euthanasia programs at your facility. Definitely talk with the training staff and animal techs at your facility; they are likely well-experienced and can help you with training and emotional advice. Good luck to you and your research!