The dachshunds yapped "at" or "about" his feet.

The answer is 'yes' provided you understand that 'about' also conveys a picture of the dogs running round or being distributed around, whereas 'at' does not specifically suggest that picture.. In fact 'at' is potentially ambiguous because it could also imply 'feet' being the focus the 'yapping' and we don't know who the owner of the feet is.
Like all one sentence questions, the absence of context can result in a range of answers, hence ( if you are interested) the development of discourse grammars, rather than single sentence grammars.

"At" suggests they are about to attack his feet. "About" sounds like they are running around yapping, which is something small dogs are known to do.

Fresco's answer is correct, and I don't contradict him.

You may consider about to be a synonym for around in this situation.

'About' for 'around' is a little British/bookish/old fashioned. If a man were attacked by a group of ruffians and he had a club he might lay about himself with it.

Shakespeare (Julius Caesar)

CAESAR
(aside to ANTONY) Let me have men about me that are fat,
Sleek-headed men and such as sleep a-nights.
Yond Cassius has a lean and hungry look.
He thinks too much. Such men are dangerous.