Regarding the sharpening stone oil, I can’t say. I don’t think it would be a good idea, but I don’t know what’s in it. As long as it’s not petroleum based, there should be little concern about how it may affect plastics. Then again, there are some petroleum based lubes that don’t bother plastics used in yoyos.
Regarding the skateboard cream, based on the term “cream”, it might be too thick. I’m sure it will behave like a thick lube but will most likely take a lot longer to break down.
I don’t really see how either will permanently damageyour bearing. Worse case is use mineral spirits to clean it out and then use a lube that is better suited for the task. I recomment YYJ Jam Oils, both thick and thin(depending on what you need) and One Drop’s VM4.