“is baby oil is good to protect your razor blade and is it good to to oil the strop?”

Yes, you can, Ballistol is made from mineral oil and other additives. Many saddle makers and leather tooling artist who go through gallons of the stuff, recommend Olive oil. Both Food grade Mineral and Olive oils are commonly used in cosmetics and many other products for human consumption.

I use Ballistol and or Olive oil. The trick is to use oil sparingly and not apply by rubbing with your bare hand, you are just rubbing grit into your strop. There are tons of post on how to properly re-hydrate a strop.

Cleanliness of a strop is probably more important to finish stropping quality than the amount of hydration. Proper cleaning, hydrating, and rolling a leather strop can dramatically improve a strop’s performance. It is the final polish on your razor’s edge, prior to touching your face.

Also do not overlook the ability of clean linen to polish the bevel and edge of a razor. For maintenance of an edge, it is or can be more of a factor than most leather strops. Used in concert it is the best of both worlds.