I think it would be worth playing around with a few other versions of “he” or “Vader”, because I think it will give the helmet a little more context and fit in better with Snoke and Kylo’s conversations regarding him living up to Vader’s legacy. Have you tried pulling from the Lego game and TROS as well?
I don’t think the ‘you’ in, “Show me, Supreme Leader, and I will finish what you started” would be interpreted as referring to Vader. It seems clearly referring to the Supreme Leader in this sentence. I guess ‘you’ could be be used in a plural noun in this context, as in “you, Vader and Palpatine” or whatever, but I don’t think most people will interpret it that way. I could even see some people being confused and thinking he is referring to Vader as Supreme Leader.
Also, I think Kylo saying he will finish what Snoke started brings up questions about him that are never really answered. What did Snoke start? Destroying Luke’s Jedi? Technically Kylo Ren did that.
I know I’m probably overthinking it but I think changing it, if you can, would just help clarify the scene more.