Parser and Apex are both correct, Vil.
You have, yet again, come up with an expression that may have been used by a native speaker once. if you hunt long and hard enough, you may even find more examples. They will still sound very unnatural to most of us native speakers.
I agree with all TP's suggested options. and would add another: 'keep a low profile'.
'Shady' tends to be used today with an implication of illegality: a 'shady customer' is a person who isn't trustworthy, and 'shady dealings' are transactions that are 'kept dark' because they bend or break the rules or the law.