When making the final cut of Blade Runner, they did something like that to fix a line. The line was one thing, but Harrison's lips said something different.
They fixed it by recording the line with his son, and pasting the result over Harrison's mouth and jaw. His son's facial structure was nearly a perfect match. I'm glad they did that instead of CGI, because no one has been able to a human face look realistic yet. It's always a little off.
Frakes is older and rounder now, so it wouldn't have worked. Upscaled SD beats bad CGI in this case.
If did occur to me that Paramount could get Frakes in for a few hours, dye his beard black, take a few years off his face with make up, put him in front of a blue screen, and get him to re-record the line while capturing his mouth movements in HD. His lip movements could then be digitally pasted on to his HD face on the Battle Bridge shot, with any necessary cleaning up around his face being a fairly simple job.
If they went down the CGI lips route, there's already the SD template of Frakes saying the line. Only his lip movement would have to be recreated in HD and applied to his HD face. Given that it's shot from relative distance in a dark environment, I think either of the above could be done successfully without it showing.
My earlier idea about just pasting his SD lips over doesn't really work due to framing, colour and lighting differences. The framing differences between the SD video and HD film mean that Frakes is slightly smaller on screen in HD, ie his mouth his bigger is SD and won't fit his HD face properly without being digitally resized.