Is it a bad idea to put hair removal cream around the penis?

Yes: Near the base of the penis and lower belly/groin it is ok, but the head and shaft are very sensitive tissue, and the hair removal cream may be quite irritating or painful. Use extreme caution.

Penis: I would not recommend using a chemical depilatory cream anywhere near the penis, scrotum or anus. I have seen countless people with chemical burns to these areas over the years. Careful use of a safety razor in these areas is much less likely to cause you problems.