If it's just the method of administration you don't like, you can ask if they'll give it to baby orally. Although, I must point out that it's normally given intramuscularly (IM injection) because the absorption is better via that method.
Anyway, it's given prophylactically. They won't know whether or not your baby has a Vitamin K deficiency and would be prone to haemorrhagic disease of the newborn. But it was felt that this was a regular enough occurrence (due to Vitamin K dependent coagulation in the classic onset, 1:100 births) to make Vitamin K a standard (although consented) procedure.
Personally (and as a neonatal nurse), I'm not hesitating to give consent for my baby to have Vitamin K by injection. I've given Vitamin K to my patients many times and have never had a problem with it. For a term baby with a normal birth weight, the dose tends to be 0.1ml (0.1cc for the North Americans) of Vitamin K (Konakian is the only brand I've seen). That in itself is a minuscule amount and is not diluted with anything else.