I think this has been discussed before, but here's my take on it.
Baby oil is pretty thick and makes you smell like a freshly changed baby's butt, which, after all the years that have passed, i don't even like to think about.
I use Neutrogena Light Sesame Body oil almost every time I shave my head.
A light coat, then shave cream on top of it, and a Headblade then a Fusion to finish off, works very well.
I have never had a clogged blade with either razor with it. I put a light coat of Neutrogena on my head when done, a nice shine and not too oily.
It costs a bit more than just Baby oil, but is much lighter and after a nice shave, the wife or significant other might just want to apply some of it on your back, front, upper, and, well, you get the idea.
If you want to stay with the baby oil, I would suggest just good ol' mineral oil. That's all baby oil is, with the fragrance. A lot cheaper and you don't smell like 'Baby's Butt"