If you don't know what APE is it's probably best to either check first or not give advice!
APE is most likely Monkey's Audio lossless format (people also use APE to refer to LAME's --alt-preset extreme). Monkey's Audio file have the extension .APE.
Converting from a lossless format to a lossy format is perfectly fine.
My best recommendation to transode would be
foobar - using either iTunesEncode or
foo_naac. Take a look on
Rarewares for some AAC encoders, including iTunesEncode.