700 x 25 Clincher on a 13mm ID Rim?

I am restoring an early 90s Serotta with Mavic wheels that measure 13mm ID inside the rim walls and 19mm OD. This used to have 23s. I have seen some charts that the max on a 13mm ID rim is a 25 size clincher. However, I have learned not to believe what I see on the internet (the sage folks on this site being an exception). Can I go to 25s without having the dreaded ice cream cone effect or stay with the 23s? With the new Conti 5000 series out there are some deals on the Conti 4000 series. The Michelins look good too. Thanks