If the birth is low trauma for the baby (no forceps) and the baby is full term and the baby gets plenty of colostrum (lots of Vit. K in colosrum), there should be no need for a supplement. So with 2 of mine, I didn't give them any Vit. K.
There was one study (and I emphasise the ONE, because one study means nothing), that suggested injected Vit. K might be risky. So one of my babies got oral Vit. K.
By the time I got to baby 4, the possible hazard of injected Vit. K hadn't been confirmed by further research, so I decided baby 4 could have injected K (even though he met all the low risk factors, brain bleeding seemed like an easy risk to not take).
Jab meant it was over & done with at birth, with oral you have to remember to give them another dose later (& that's easy to forget to do).
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Or in short, I'd get an injection if I were you! But good luck, whatever you do.