# we have rejected secret and shameful ways

This means that Paul and his coworkers refuse to do "secret and shameful" things. It does not mean that they had done these things in the past.

# secret and shameful ways

"the things that people do secretly because they cause shame" 

# walk in craftiness

"live by deceiving people" 

# we do not mishandle the word of God

"we handle God's message correctly" or "we use the word of God properly" 

# we recommend ourselves to everyone's conscience

This means that they provide enough evidence for each person who hears them to decide whether they are right or wrong.

# in the sight of God

"before God" or "with God as witness"