Not sure but..., SCSW-4th on page 307 shows that the 629 Classic started in with the 629-3 in 1990. On page 308, it lists the Classic Hunter that came in the 629-1 engineering change, but that had an unfluted cylinder. So, no luck there.
I can say that the 629-1's, without the underlug of the classic, that I have observed all had wood stocks, earlier with football cut and later with speed loader cut. All of the 629 Classics I have observed, and all the ones I own, came with different versions of Hogue grips.
Probably safe to say it came with those Hogues, but to know for sure, you're going to need the letter. Best of luck to you!