It depends on how you "route" the payments.
Are they at any point in a personal or corporate bank account that you control? If so, the bank from which you route the payments is aware that you are a US citizen, they are likely doing some form of reporting under FATCA, meaning the IRS is or theoretically can become aware of your account and thereby estimate your income level. When your next tax return doesn't match that, they may start digging into it. This can lead to prosecution, which isn't really effective if you're overseas (and not that big of a target). But one issue that could arise is that next time you go to renew your passport, it's refused because of an outstanding tax debt.
If the payments are going directly from the affiliate network's bank accounts to you, then directing the payments to your wife's accounts is less likely to become known to the IRS. It's probably a good idea if the affiliate accounts are in her name as well.
US taxation is something you don't want to get wrong, though, so run it by a US tax attorney.