If he hasn't got any particular aims to achieve in that world, it might not matter that much. Better keep it secret. If the info happened to leak, he would be captured by some royals, nobles, magic organisation, slavers, corrupt merchants, evil church, demons, you name it, to be used as an extremely convenient tool. It does cause him occasional trouble to keep minding his words and come up with petty lies, and it certainly will slow down his efforts to make progress, but at the end of the day, he's still making a whole lot faster progress than anyone else.