I think for clarifying that Snoke wasn’t literally controlled by Palpatine like a puppet, you could make two lines changes.

Instead of “I made Snoke”, he could say, “I trained Snoke”
The vat of Snokes would make it clear enough that he made him (unless you used poppa’s Palpatine clones shot). Maybe a shot could be made with a Snoke clone and a Palpatine clone. You could even use that shot to show other clones that are in-between the physical appearance of Snoke and Palpatine. Which would answer the question of who Snoke was a clone of: technically Palpatine, but a deformed, genetically alerted version of him. And each new clone became less deformed than the last. Snoke was just an earlier iteration.
Do what Dom did, and take out Snoke’s “you have ever heard” part of Palpatine’s line. This line definitely makes it seem like Palpatine IS Snoke.