Can strong nations maintain their power and influence without interfering with other nations' development?

No. Part of having power and influence is asserting dominance and having a say in what goes on in things outside of you. It is possible to have power that exist inside oneself but then you have to consider the influence, and influence is asserting "yourself" over others, whether it is your beliefs or knowledge. So, no it overall isn't possible to be a powerful and influencing nation if you aren't interfering with other nations. Those other nations are what makes you powerful and influencing, a person can't be powerful and influencing without considering those around him. Same as a nation.