Keep in mind that the A in IPA just means Alphabet and just like the Latin alphabet, it can be and is used differently for different languages, and even more than one way for the same language.
Like any phonemic transcription scheme it works best with a pronunciation guide.
The problem you are facing is a mapping problem. You need to decide exactly which sound is represented by each of your CPA symbols for your language and you need to decide exactly which sound is represented by each of the IPA symbols, for each of your sources if they differ.
Then if you are lucky and both are based on similar analyses of the sound systems of the language in question you will have a 1:1 mapping of CPA symbols to IPA symbols.
But more often than not you will not be quite this lucky and one scheme will have more symbols than the other scheme. This is where you will have to make decisions based on your knowledge of phonetics and phonology.