Daniel to repeat I don't mean to be critical of you for calling it that, because I know many people fluent in philosophy do so. Categories can be useful things and I understand why they want to put Epicurus in that box. However my personal preference is dealing in a world of non-professional philosophers who are looking for practical ways to organize their lives. You are right that the "pleasure" focus is only a part, but an important part, of Epicurus, but what distinguishes him almost as much are his positions on the universe being natural/non theistic (atomism) and his views on the role of reason and the senses in his epistemology.
I'm mainly just saying that in the circles I come into contact with it is confusing to use the term hedonism, especially since its connotation in English is so negative. The word carries no positive connotations whatsoever in my mind, or in the minds of people I generally deal with. That's unfortunate, but since there is no evidence that the ancient Epicureans used the word to describe themselves, I see no reason to fight a battle over that word when there are so many other battles to fight.
Beyond the rhetorical considerations, I really don't think that Epicurus himself would approve of it. The role of pleasure in ethics is certainly an important conclusion, but I feel sure that he considered his conclusions on how to think, and how the universe operates, to come before his contributions on ethics. I gather that the experts think that the letter to Herodotus was the first in time that he wrote, and the letter to Menoeceus probably among the latter. Herodotus, like Lucretius' poem, certainly mentions the role of pleasure, but places at least as much emphasis on the physics and epistemology.
But you're attacking an area I think is super-important: how to approach new people, and it seems to me the best way to start off with them is not to allow them to be distracted by a word that might turn them off before they've understood the other fundamentals of the philosophy.
Now I will be the first to admit that you may operate in different circles, and the new people you are talking to may have no issues with the word "hedonism" at all. So if you think that is true, you should definitely proceed in the way you think best, using hedonism.
One thing I firmly believe is true is that there is no single "best" way to pursue the promotion of Epicurean philosophy, so it is good to have alternative approaches.