The use of cell-lines from aborted babies in the development of vaccines is sadly of long standing, so the question has been asked, and answered, before. It is as you say a form of cooperation in evil, but it is ‘material’ rather than ‘formal’, and ‘remote’ rather than ‘proximate’.
The first distinction is about whether you intend the evil. If you contribute to an abortion by, saying, driving a woman to the clinic, because you want her to have an abortion, that is formal cooperation, and as serious an any kind of involvement. If you fill the car with fuel, knowing what it is for, but just because it’s you job to fill up cars with fuel, it’s ‘material’ cooperation. That can still be serious, but it is a different category.
Even material cooperation can be ‘proximate’, that is ‘close’: selling a gun to a known murderer just for the money is close cooperation, it brings you very close to the evil. Paying taxes knowing that some of the money will be used for bad purposes, or buying things in a shop whose owners make donations for bad things, is remote cooperation.
We should avoid all cooperation with evil if we can easily do so. We can’t say: we should never cooperate in the smallest way with evil, because that would be impossible. So we make another distinction, about how easy it is to avoid cooperation: between ‘grave’ and ‘slight’ ‘inconvenience’. Grave inconvenience is when, say, your job, and perhaps the welfare of family members, is put in jeopardy.
Regardless of the level of inconvenience, formal cooperation in mortal sin is always wrong, because it is itself mortal sin. By intending the sin, we make it our own.
With material cooperation, the closeness tells us the level of inconvenience one should be prepared to suffer. One can’t be exact here, but remote material cooperation does not require us to suffer grave inconvenience. Instead one should balance the good to be gained against the evil of the cooperation.
You’d find all this in any textbook of moral theology from the old days, and indeed orthodox ones from today.
It’s for you to decide how much ‘inconvenience’ changing your job would be, but the Congregation for the Doctrine of the Faith has in the past said that the level of cooperation in evil represented by being vaccinated with a vaccine developed from this cell-line is sufficiently remote to allow people to take it in order to secure the good of immunity from a serious disease, but they urged people to protest. It’s not nothing. The Bishops I think have in fact protested.
It is a question for each individual how important the good of immunity is in itself. Your question though is also about administering the programme of giving the vaccine, so the question is about the good, to you and others, of this particular job.
The old text books used an example of a Catholic type-setter who found himself being asked to set type for a pornographic book. If his family depended on his income, he should look for another job before leaving the present one. In other words, he can put up with this level of cooperation in evil at least in the short term. Whether it is possible to escape even in the longer term depends on other things. Are there any jobs where we will not be asked to cooperate in this kind of thing, that we can actually get? Certainly, there are fewer than there used to be.
The major magisterial document on the issue is the Congregation for the Doctrine of the Faith's Instruction Dignitatis Personae (2008).
Some useful information was included in an article in the Irish Catholic by Dr Helen Watt (she comes to very much the same conclusion as I do):
It needs to be said at the outset that foetal cell-lines are not the same as actual foetal parts or tissue. Such tissue was itself sourced from historical abortions: a horrifying practice involving close complicity with those performing the abortion. The tissue was then used many years ago to make various cell-lines that circulate in labs today and are used in developing some vaccines. Although in the case of the HEK 293 cell-line there is some possibility that it may have come from a miscarriage, I will assume that this cell-line too originated, as seems all too likely, from a deliberate abortion.
Foetal cell-lines are developed from the original cells or tissue: they do not include any cells of the unborn child. It is also worth noting that where they are used for vaccines, these cell-lines are used not as intended ingredients (even if some fragments of cells remain) but to prepare the vaccine in or e.g. to test it on.
The Covid-19 vaccine candidates range from those that did not involve foetal cells at any stage (for example, CureVac), to those that used foetal cells at every stage: design, testing and production (for example, Astra-Zeneca). Other vaccines again (for example, Pfizer) do not use a foetal cell-line in ongoing production, but did use one in confirmatory tests.