Personally, I wouldn't use a vegetable oil, just due to them going rancid over time. But that is neither here nor there.
As for any sort of oil (neetsfoot, mineral, or PJ) they will make the leather hold the compound a bit better. Its common when using powdered compounds to mix them with something to apply them, mostly to avoid dust. The main thing is getting a good bond. So as mentioned, starting with warm leather and then making sure that whatever carrier the compound is in is well bonded to the leather is what you want. Its probably some form of wax, though I've seen some polishing rouges that seem to be more of a chalk. Either way, the goal is to keep it bound to the leather, and very dry leather isn't as good at that. ( I re-read my other post, I was mistaken, I have oiled some leather compounded strops, but it had nothing to do with the compound as such, it was just to keep the leather from drying out, or absorbing moisture and molding. The compound I was using had a wax base and bonded well to the leather.)
What you also don't want is over-oiled leather, as it will get soft, stretchy and probably start to curl (if its a hanging strop) Over time, leather does dry, so applying a bit of oil is also worth doing. Your local conditions, and what you have available is going to play a part in what you choose. I know I keep saying oil, but anything that is going to keep the leather soft, and adhere the compound is really what you are looking for. In my case, living in a rather warm, high humidity environment, I've used different stuff that I did when I was living in a dry cold place. So long as you are not smearing random stuff on several hundred dollars worth of latigo, go nuts, and if several hundo is well within your "lets see what happens" budget, well, then let us know how it goes. Not being sarcastic, it would be somewhat interesting to see. There is a lot of "the only way" info out there, and I bet there are far more "right ways" to do things, and some not quite wrong, just "not ideal" ways.
I've had somewhat better luck using things like neetsfoot and beeswax on leather goods in general, though some of that may well be just due to bias. I know that many guys who straight shave prep their strops with high purity mineral oil. I very much suspect its less a matter of what, than how much. Again, not saying you shouldn't use PJ, it might be really good for your conditions, just that its not special in some way.