Adding a line ruins the comedy beat him staying silent brought, and it also makes the scene too corny. Finn insists Poe take his hand and say “for Chewie” as Poe rolls his eyes (showing to the audience to not take this rejoice so seriously). And then 3PO joins and DOES take it seriously. The three of them (or just Poe, annoyed) look at 3PO strangely, because he’s a silly robot who doesn’t get it and wants to feel like he’s helping. It’s awkward on purpose. If you add him saying something with them, it takes away the awkward comedy moment, makes it more corny because now they’re all taking the “for Chewie” thing a little too seriously. And just makes it an overall forgettable moment now. I don’t think anything needs to be added here; C-3PO staying silent isn’t an issue, really. MAYBE if we can extend the shot of Poe looking frustrated at C-3PO AFTER he says “For my friend!”, then we can retain the comedy beat… but I don’t know. 3PO saying anything distracts us from Poe’s annoyed expression.
Perhaps have 3PO say a line as he’s walking over. So the silent part of Poe being annoyed is still retained. But everyone seems to be adding the line to fill in this silent gap, so I dunno haha.

Little word-y there, but I hope you get my point. And to be fair, Finn and Rey are taking the hand thing and “for Chewie” seriously. So maybe everyone sees it differently. Just overall not really feeling this change. It was perfectly, awkwardly C-3PO.