I agree with
@Preitler @RabbitsOfTheCreek and
@eco2pia. It is nonsense to say the mother rabbit will abandon handled babies. Domestic rabbits are usually incredibly tolerant, even uninterested in their babies, but for once or twice a day feedings. You can pull the nest box for most of the day, only returning it for feedings (called "shelving"), swap foster babies in and out of boxes (no Vick's or other distracting smells needed), pull the babies out of one box and replace it with another (usually cleaner) box, etc.
Of course there is variation among does and some are more nervous or spend a lot more time checking on the nest, etc. But I have yet to have a doe reject a foster baby, and I usually simply plop them into the box without spending any effort getting it to smell like the others. Sometimes a doe will have the babies on the wire, and it is necessary to gather them up and put them in the box by hand; no rejection. As a matter of fact, last month I had a doe have them on the wire, and they all fell out onto the ground below. Pretty gross, but they all survived due to being able to burrow into the warm composting manure under the cages. We spent two full days finding newborns and popping them into one or the other of several nest boxes, with no issues. But you can be sure they smelled like a little of everything, both human and rabbit!
In fact, I handle kits briefly every day, starting the day they are born. Not only does it help me keep track of their health and development, and I can find and remove dead kits before they become a problem, but it also produces much calmer, more easily handled bunnies. In effect, slightly stressing them eventually stress-proofs them. The neurological basis is fairly well-known thanks to the US Military's "Super Dog" program. Here is a good overview of the idea:
https://breedingbetterdogs.com/article/early-neurological-stimulation
That said, overly-bothered mother rabbits can and will abandon or kill a litter. So, while I've had rabbits that were not at all tame do fine with my handling their kits, it behooves a breeder to try to make sure the doe is used to attention. I do spend a fair amount of time with my rabbits, not necessarily picking them up but talking to them and petting them. And my usual practice is to give mother rabbits a tablespoon of BOSS (black oil sunflower seeds) in a treat cup every day when I check their nest. Pretty soon they can't wait for me to come do a box-check!
