Are you sure of that b2b? As I did a test not so long ago making many putts from the fairway to test this and the result proved that putting does not wear the ball at all. (Excluding mulligans).
Just did another test with a new ball and did 15 putts along the fairway. This is the wear indicator after the test...
↓↓ EDIT : You're welcome mkg, thank you. : ) ↓↓