Are 乒 and 乓 used in classical chinese? 乒乓 is the modern word for ping pong, based around onomatopoeia (and similarity to 兵 for phonetic element) and, as some people claim, shape. I was wondering if this shape explanation is true, or little more than a folk etymology of the word.

That is to say, are 乒 and 乓 (or one of them) used in words (or on their own) other than in "乒乓"? The easiest way is to see if these were ever used in classical chinese.

If they are true historical characters, what did they mean before? Are there any words which still use them now other than in ping pong?

Quite a diverse question, but interesting to me.
The earliest texts with 乒乓 I can find is vernacular novels of Ming dynasty.

《西遊記》 Journey to the West as an example:

如此二三日，又聽得後宰門乒乓乒乓，磚瓦亂響。——Chapter 10

他掄槍舞劍，一擁前來，照行者劈頭亂砍，乒乒乓乓，砍有七八十下。——Chapter 14

乒乒乓乓，好便似殘年爆竹；潑潑喇喇，卻就如軍中炮聲。——Chapter 16

“乒” and “乓” are used together as onomatopoetic in history. :)