If Armstrong can play at an acceptable MLB level, there's no reason to worry that he too is a lefty. In fact, it would allow Ozzie to go with a set lineup with the catcher always batting in the same spot in the order. In addition, without having to worry about lefty/righty matchups, Ozzie could have the catchers start based on who is pitching for the Sox, so that each starter gets comfortable working with one catcher.
The universe is the practical joke of the General at the expense of the Particular, quoth Frater Perdurabo, and laughed. The disciples nearest him wept, seeing the Universal Sorrow. Others laughed, seeing the Universal Joke. Others wept. Others laughed. Others wept because they couldn't see the Joke, and others laughed lest they should be thought not to see the Joke. But though FRATER laughed openly, he wept secretly; and really he neither laughed nor wept. Nor did he mean what he said.