Honour Among Dishonour

In short: don't.
Don't cooperate with defectors. Don't treat the honourless with honour. 

"

Who should I swear by? Thou believest no god:
That granted, how canst thou believe an oath?

And Aaron essentially replies, indeed, an oath from me is worthless. But I know that you have a belief in morals and ethics. I know that if you give me your word, you’ll keep it,

For I know thou art religious
And hast a thing within thee called conscience.

"

Your conscience should tell you this: betray him as flagrantly as you can. Whenever possible, offer leeching or sabotage to the honourless. Trickery is not forbidden, it is mandatory. Let the honourless be deprived of everything. Keeping your promises to them doesn't make you upstanding, it makes you an idiot.

Unless it benefits you, of course. Self-sacrifice should be the opposite of your principle when dealing with the unworthy.