Pointlessly cynical view. If people start laundering money for the sake of a cycling team (which is simply just vanity) then it's at their own risk. The likelihood is, especially looking at who the owners are now, that it can be controlled to a good extent. Either way, would be considerably better than what we have now...
Salary caps are only barely enforceable in sports where teams are large, stable, entities and everyone is based in one jurisdiction. Even in those circumstances there are various schemes to circumvent them, which are occasionally discovered and mostly are not. Getting around a salary cap is not money laundering and does not have to involve criminality.
Teams are largely owned or financed by a collection of oligarchs of dubious character, some of whom exercise a great deal of political power (like the torture-princeling of Bahrain). Riders largely live in tax havens or to put it more politely countries that offer a great deal of protection for the privacy of personal finances.
The UCI simply has no way to regulate this.