They actually could do it.
Keep Picard as captain, he's always been a thinking mans captain and not a physical one, and he could do the job just fine, he still looks almost the same as he did back then.
Replace the XO with someone young, Frakes can cameo as captain of Titan, so it's a good chance to lower the average age. Get someone in around Chris Pines sort of age
Keep Worf, if Dorn hits the gym, with all the makeup you will never know the difference.
Keep Geordie, Levar is in fantastic shape, he looks fine
Replace Troi and Crusher with "younger models" sorry but they would have to to bring in an audience. Troi is with Riker, and Crusher transferred somewhere.
Data is gone, so replace him again with a younger crewmember.
This way really the only "old" one is Picard, and as I say that really shouldn't be a huge issue. We have a nice mix of familiar faces, and young blood.
It's do-able but it won't happen.