I'm a marginally successful ML whitetail hunter so take this for what it's worth:
Ballistol does have a distinctive odor, which I find slightly unpleasant. There are many rust inhibitors today, like RIG, Break Free/CLP, and Kleen Bore's "RustGuardit" none of which are period correct but are highly effective if you want to protect your firearm in rainy, wet conditions.
I've not seen a whitetail that was spooked by a scent, usually it is noise or motion. I've observed several walk up to and past my tractor, left in a field, without giving a second thought.
Patches can be made using strips of fabric, soaked with a Ballistol mixed with water, about 1/6 or 8/1, patches in a plastic bag for a day, hung to dry, then cut to size. They are easy to handle and my testing shows they are equal to or better than patches lathered with concoctions of beeswax, lard, oil soap, mink oil, etc.